MRC antenna diversity for FM IBOC digital signals

ABSTRACT

A method for processing a radio signal includes: receiving a signal on two antennas; demodulating the signal using first and second independent signal paths that are synchronized by symbol number; maximum ratio combining branch metrics from the two receiver paths; and using the combined branch metrics to produce an output, wherein the receiver paths include an arbitration scheme. A receiver that implements the method is also provided.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of U.S. patent applicationSer. No. 13/536,203, filed Jun. 28, 2012, and titled “MRC AntennaDiversity For FM IBOC Digital Signals”, which claims the benefit of U.S.Provisional Patent Application No. 61/556,428, filed Nov. 7, 2011. Bothof these applications are hereby incorporated by reference.

BACKGROUND

iBiquity Digital Corporation's HD Radio™ system is designed to permit asmooth evolution from current analog amplitude modulation (AM) andfrequency modulation (FM) radio to a fully digital in-band on-channel(IBOC) system. This system delivers digital audio and data services tomobile, portable, and fixed receivers from terrestrial transmitters inthe existing medium frequency (MF) and very high frequency (VHF) radiobands. Broadcasters may continue to transmit analog AM and FMsimultaneously with the new, higher-quality and more robust digitalsignals, allowing themselves and their listeners to convert from analogto digital radio while maintaining their current frequency allocations.Examples of waveforms for an FM HD Radio system are shown in U.S. Pat.No. 7,724,850, which is hereby incorporated by reference.

A variety of antenna diversity techniques have been developed anddeployed for use with automotive FM receivers. They are used to mitigatethe effects of distortion and outages due to multipath propagation ofthe received FM signal, and can also accommodate the directionalcharacteristics of glass-embedded window antennas. All diversitytechniques use two or more antenna elements, and some require multipletuners/receivers. Some techniques can be applied to digital signals, andsome cannot.

Blind diversity switching can be economically attractive because asimple multi-position switch connects the selected antenna element toonly one tuner and receiver. However, because the switching is blind,there is no guarantee that the next antenna element will carry a bettersignal, and subsequent switching may occur in rapid succession until agood signal is found. Furthermore, since the digital signal iscoherently detected and tracked, each antenna switching event is likelyto cause symbol corruption and temporary loss in channel stateinformation (CSI) and coherent tracking.

Such switching transients can be avoided by using a smooth diversitycombining algorithm. These techniques involve some kind ofmultiple-input signal combining (pre or post-detection), and requiremultiple tuners. One combining method for analog FM signals employsphase diversity using a constant-modulus algorithm (CMA). However, thisapproach is not valid for HD Radio signals as the digital sidebands arenot characterized by a constant envelope.

IBOC HD Radio receivers can be used in combination with switch diversityantenna systems. However the use of switch diversity antennas introducesabrupt transients in the coherent tracking of the digital signal, whichdegrades digital performance.

SUMMARY

In one aspect, the invention provides a method for processing a radiosignal. The method includes receiving a signal on two antennas;demodulating the signal using two independent signal paths that aresynchronized by symbol number; maximum ratio combining branch metricsfrom the two signal paths; and using the combined metrics to produce anoutput, wherein the receiver paths include an arbitration scheme.

In another aspect, the invention provides a receiver including first andsecond inputs configured to receive a signal on two antennas; first andsecond demodulators for demodulating the signal in first and secondindependent signal paths that are synchronized by symbol number; andcircuitry for maximum ratio combining branch metrics from the two signalpaths, and using the combined metrics to produce an output, wherein thesignal paths include an arbitration scheme.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a high-level Maximum Ratio Combining (MRC) block diagram.

FIG. 2 is a functional block diagram of a receiver configured to includeFM phase diversity and digital MRC.

FIG. 3 is a functional block diagram of a receiver configured to includeeither diversity (MRC and FM phase diversity) or a data scanningreceiver.

FIG. 4 is a functional block diagram of a receiver configured to includeboth diversity (MRC and FM phase diversity) and a data scanningreceiver.

FIG. 5 is a functional block diagram of a receiver configured to includeboth diversity (MRC and FM phase diversity) and a data scanningreceiver, also with MRC.

FIG. 6 is a functional block diagram showing a computation for ViterbiBranch Metrics.

FIG. 7 is a functional block diagram showing a computation for ViterbiBranch Metrics.

FIG. 8 is a graph illustrating the effects of warping of Viterbi BranchMetrics.

FIG. 9 is a representation of branch metric scaling and quantization.

FIG. 10 is a functional block diagram illustrating a process forproducing a digital signal quality metric.

FIG. 11 is a functional block diagram of a filter circuit.

FIG. 12 shows the spectrum of a Highpass Halfband Filter.

FIG. 13 shows the magnitude spectrum of the pre-acquisition filter.

FIG. 14 is a functional block diagram of the quality metric computation.

FIG. 15 is a flowchart for the acquisition of the digital signal.

FIG. 16 shows the probability of a good acquisition.

FIG. 17 shows the probability of a bad acquisition.

FIG. 18 is a plot showing the average time required for subframe lock.

FIG. 19 is a plot of bit error rate.

FIGS. 20 through 24 are plots of a digital signal quality metric.

FIG. 25 is a state diagram for MRC coordination and arbitration.

DETAILED DESCRIPTION

Maximum Ratio Combining (MRC) of Viterbi Branch Metrics (VBMs) canafford improved signal to noise ratio (SNR) performance, at the cost ofadding a second digital reception path (from tuner to baseband). An MRCreceiver is intended to operate at lower SNRs than a single receiver,and the acquisition and tracking algorithms designed for a singlereceiver may not operate effectively at these lower SNRs, compared to asingle demodulator. Furthermore, if one of the demodulators isoutputting corrupted Viterbi Branch Metrics (due to a poor antennasignal) while the other demodulator is correctly demodulating, thencontamination is possible, which degrades combined performance.

Various techniques for implementing Maximum Ratio Combining in anantenna diversity system are described herein. Such techniques areapplicable to processing of an OFDM signal of an HD Radio FM IBOC radiosystem. In the embodiments described herein, MRC involves the combiningof Viterbi Branch Metrics (derived from the demodulated symbols) fromtwo (or possibly more) diversity receiver paths, also referred to hereinas signal paths. Each of these receiver paths includes a tunerconfigured to receive a signal from a diversity antenna element, an OFDMdemodulator, and Viterbi Branch Metric computation for each receiveroutput symbol (code bit). The combining or adding of the Viterbi BranchMetrics is the MRC function. The combined Viterbi Branch Metrics canthen be deinterleaved, decoded and processed as in the subsequentfunctions of a conventional single receiver. Existing HD Radio receiversalready compute appropriate branch metrics, including signalequalization and noise normalization, which can be used as describedherein.

Assuming independent fading at each antenna element, MRC combines branchmetrics from two different receiver paths to minimize receiver bit errorrate (BER). Branch metrics are effectively a measure of thesignal-to-noise (energy) ratio of each demodulated symbol at the inputto a Viterbi decoder. The MRC algorithm sums corresponding, synchronizedViterbi Branch Metrics from two receiver channels prior todeinterleaving and Viterbi decoding. FIG. 1 is a block diagram ofportions of a receiver 10 connected to two antennas 12, 14. The receiverincludes two signal paths 16, 18 (also called receiver paths orchannels). The first signal path 16 includes a first radio frequencyfront end/tuner 20 and a first demodulator 22. The second signal path 18includes a second radio frequency front end/tuner 24 and a seconddemodulator 26. The antennas are configured to receive an in-band,on-channel (IBOC) radio signal, which can be an FM HD Radio signal. HDRadio signals are described in, for example, U.S. Pat. No. 7,933,368,which is hereby incorporated by reference. Each signal path includesprocessing circuitry or a processor programmed to compute Viterbi BranchMetrics for each receiver output symbol. In the example of FIG. 1, suchprocessing circuitry or a processor can be included in the demodulatorblocks.

The antennas can be elements with different characteristics, positionedat different locations, and/or positioned at different orientations. Thedemodulators produce Viterbi Branch Metrics on lines 28 and 30. TheseViterbi Branch Metrics are maximum ratio combined in combiner 32. Thecombined metrics are then passed to circuitry 34 that processes thecombined metrics to produce an output signal on line 36. This processingcircuitry may include a deinterleaver, decoder, codec, etc. as is knownin the art.

MRC is attained by adding the corresponding Viterbi Branch Metrics ofthe demodulated symbols (bits before decoding) from the two receiverpaths. Corresponding VBMs from the two receiver paths can besynchronized, as shown by line 38, by indexing prior to thedeinterleaver. The indexing is used to unambiguously identify and label(number) the symbols in the interleaver matrix. Like-indexed VBMs areadded when the corresponding symbols are available from both receiverpaths. The embodiment of FIG. 1 uses two independent receiver/demods,then identifies and combines like-indexed symbol Viterbi Branch Metrics.The indexing allows the two receiver paths to operate asynchronously.

When one of the receiver paths has no VBMs available, the missing VBMsare assumed to be zero, and only the receiver path with valid VBMs isused (no addition is necessary). When VBMs are not available from eitherreceiver, the downstream functions (deinterleaver, Viterbi decoder,etc.) are reset, assuming for example, a reacquisition process isinvoked.

A baseline MRC technique assumes that each receiver path is configuredto independently acquire and track the signal, and that the branchmetrics are aligned and combined. In one case, performance is nearoptimum when both receivers are tracking the signal with propersynchronization. The main performance enhancement is achieved in dynamicfading conditions. When one antenna is in a deep fade, the other antennamay not be faded, and vice versa. Symbol and frequency tracking for eachreceiver path can flywheel over short fades or outages. The flywheelingmaintains adequate synchronization during brief signal outages.

Analog FM phase diversity can be implemented using two antennas, twotuners, and two FM receiver paths. A pair of signals can be combinedprior to the FM demodulator using a Constant Modulus Algorithm (CMA), orsome variation thereof. Since two antenna signal paths are available,these phase diversity systems are compatible with MRC for IBOC digitaldiversity.

FIG. 2 shows a functional block diagram of an implementation of digitalMRC in a vehicle application that also employs analog FM phasediversity. FIG. 2 is a block diagram of a receiver 40 connected to twoantennas 42, 44. The receiver includes two signal paths 46, 48. Thefirst signal path 46 includes a first radio frequency front end/tuner50, an analog FM demodulator 52 and a first digital demodulator 54. Thesecond signal path 48 includes a second radio frequency front end/tuner56, the analog FM demodulator 52 and a second digital demodulator 58.The antennas are configured to receive an in-band, on-channel radiosignal, which can be an FM HD Radio signal. The antennas can be elementswith different characteristics, positioned at different locations,and/or positioned at different orientations. The demodulators produceViterbi Branch Metrics on lines 60 and 62. These VBMs are maximum ratiocombined in combiner 64. The combined metrics are then passed tocircuitry 66 that processes the combined metrics. This processingcircuitry may include a deinterleaver, decoder, codec, etc. as is knownin the art. An audio decoder 68 produces digital audio and blend controlsignals as illustrated by line 70. The analog FM demodulator 52 includesFM diversity processing 72 and FM demodulation 74 to produce ademodulated FM signal on line 76. A blend control 78 blends thedemodulated FM signal on line 76 and the digital audio signal to producean audio output on line 80. Each receiver path is configured tocalculate the branch metrics and to independently acquire and track thesignal, and ensure that the branch metrics are aligned and combined.

MRC is attained by adding the corresponding VBMs of the demodulatedsymbols (bits before decoding) from the two receiver paths.Corresponding VBMs from the two receiver paths can be synchronized, asshown by line 82, by indexing prior to the deinterleaver.

FIGS. 3 through 5 show several implementation options for including MRCin a data scanning receiver. FIG. 3 shows how a receiver 90 with twoantenna signal paths can be configured to use the second antenna signalpath for either MRC and phase diversity, or for a non-MRC scanning datachannel, but not both simultaneously. The receiver 90 is connected totwo antennas 92, 94. The receiver includes two signal paths 96, 98. Thefirst signal path 96 includes a first radio frequency front end/tuner100 that can be tuned to a first frequency, and a first digitaldemodulator 102. The second signal path 98 includes a second radiofrequency front end/tuner 104 that can be tuned to either the firstfrequency or a second frequency, and a second digital demodulator 106.The antennas are configured to receive an in-band, on-channel radiosignal, which can be an FM HD Radio signal. The antennas can be elementswith different characteristics, positioned at different locations,and/or positioned at different orientations. The demodulators produceViterbi Branch Metrics on lines 108 and 110. These VBMs can be maximumratio combined in combiner 112. The combined metrics are then passed tocircuitry 114 that processes the combined metrics to produce an outputsignal. This processing circuitry may include a deinterleaver, decoder,codec, etc. as is known in the art. Alternatively, instead of MRC,additional processing circuitry 116 can be provided to process theoutput from the second digital demodulator to produce a data output online 118. The tuner outputs are subject to FM diversity processingand/or analog FM demodulation as shown in block 120 to produce an analogaudio signal on line 122. The analog FM audio signal and a digital audiosignal on line 124 are blended as shown in block 126 to produce an audiooutput on line 128. Each receiver path is configured to calculate thebranch metrics and to independently acquire and track the signal, andensure that the branch metrics are aligned and combined.

FIG. 4 is a block diagram of a receiver 130 that includes many of theelements of FIG. 3 and adds a third signal path 131. The third signalpath includes a third tuner 132 and a third digital demodulator 133 toenable both MRC and phase diversity as well as a non-MRC data scanningchannel. The output of the third digital demodulator is processed byprocessing circuitry 134 to produce a data output on line 135. In thisexample, two of the three tuners are tuned to the same frequency.

FIG. 5 is a block diagram of a receiver 136 that includes many of theelements of FIG. 4 and adds a fourth signal path 137. The fourth signalpath includes a fourth tuner 138 and a fourth digital demodulator 139 toenable MRC on both the main receiver signal as well as the scanning datapath. The Viterbi branch metric outputs of the third and fourth digitaldemodulators on lines 140 and 141 are combined in combiner 142. Then thecombined signal is processed by processing circuitry 143 to produce adata output on line 144. In this example, both the first and secondtuners are tuned to a first frequency, and both the third and fourthtuners are tuned to a second frequency.

I. Viterbi Branch Metrics

The Viterbi Branch Metrics (VBMs) for the described IBOC MRC embodimentsare a ratio of the estimated signal to noise energy of the channelsymbols (bits) prior to deinterleaving and decoding. These VBMs can becomputed as described in U.S. Pat. Nos. 6,982,948, 7,305,056 or7,724,850, which are hereby incorporated by reference. The first twopatents (U.S. Pat. Nos. 6,982,948 and 7,305,056) use linear filters toestimate Channel State Information (CSI).

As shown in U.S. Pat. No. 7,305,056, an HD Radio signal includes ananalog modulated carrier and a plurality of digitally modulatedsubcarriers. Some of the digitally modulated subcarriers are referencesubcarriers. FIG. 6 is a functional block diagram describing the CSIestimation using linear filters as shown in U.S. Pat. No. 7,305,056.FIG. 6 illustrates a method of estimating both the phase reference andthe CSI from the reference subcarriers in an HD Radio signal. Thereference subcarriers can be used for acquisition, tracking, estimationof CSI and coherent operation.

As shown in FIG. 6, the complex training symbols carried by thereference subcarriers are input on line 148 and the complex conjugate ofthe symbols is taken as shown in block 150. The complex conjugate ismultiplied with a known training sequence on line 152 by multiplier 154.This removes the binary (±1) timing sequence modulation from thereceived training subcarriers by multiplying them by the synchronized,decoded, and differentially-reencoded BPSK timing sequence. Theresulting symbols on line 156 are processed by a finite impulse response(FIR) filter 158 to smooth the resulting symbols over time, yielding acomplex conjugated estimate of the local phase and amplitude on line160. This value is delayed by time delay 162 and multiplied by anestimate of the reciprocal of the noise variance on line 164 bymultiplier 166. The noise variance is estimated by subtracting thesmoothed estimate of the local phase and amplitude on line 160 from theinput symbols (after appropriate time alignment provided by delay 168)at summation point 170. Then squaring the result as shown in block 172,and filtering the complex noise samples as illustrated in block 174. Thereciprocal is approximated (with divide-by-zero protection) as shown inblock 176. This CSI weight is interpolated over the 18 subcarriersbetween pairs of adjacent training subcarriers as illustrated by block178 to produce resulting local CSI weights on line 180. The CSI weightsare then used to multiply the corresponding local data-bearing symbolsreceived on line 182, after they have been appropriately delayed asshown in block 184. Multiplier 186 then produces the soft decisionoutput on line 188.

In FIG. 6, lines carrying training symbols are labeled T and linescarrying data are labeled D. In addition, filter 174 includes a delayof:

${{delay} \geq \frac{1}{\beta}},{{{where}\mspace{14mu}\beta} = \frac{1}{16}}$and, y_(n, m) = 2 ⋅ (1 − β) ⋅ y_(n − 1, m) − (1 − β)² ⋅ y_(n − 2, m) + β² ⋅ x_(n, m).

These expressions relate to a 2-pole IIR filter with a time constant β.The IIR filter computes smoothed output samples “y” from input sample“x” and previous output samples.

The CSI weight combines the amplitude weighting for maximum ratiocombining along with a phase correction for channel phase errors. ThisCSI weight is dynamic over time and frequency, and is estimated for eachQPSK symbol.

${{CSIweight} = \frac{\alpha^{*}}{\sigma^{2}}},$where α* is an estimate of the complex conjugate of the channel gain andσ² is an estimate of the variance of the noise.

The operation of the CSI recovery technique of FIG. 6 assumesacquisition and tracking of the frequency of the subcarriers, and thesymbol timing of the OFDM symbols. The frequency and symbol timingacquisition techniques exploit properties of the cyclic prefix. Thefrequency and symbol tracking is accomplished through observation of thephase drift from symbol to symbol over time or frequency (acrosssubcarriers).

After acquisition of both frequency and symbol timing, synchronizationto the Block Sync pattern of the BPSK Timing Sequence is attempted bycross-correlating the differentially detected BPSK sequence with theBlock Sync pattern. The differential detection is performed over allsubcarriers assuming that the location of the training subcarriers isinitially unknown. A cross-correlation of the known Block Sync patternwith the detected bits of each subcarrier is performed. A subcarriercorrelation is declared when a match of all 11 bits of the Block Syncpattern is detected. Block synchronization (and subcarrier ambiguityresolution) is established when the number of subcarrier correlationsmeets or exceeds the threshold criteria (e.g., 4 subcarrier correlationsspaced a multiple of 19 subcarriers apart).

After Block Sync is established the variable fields in the BPSK TimingSequence can be decoded. The differentially detected bits of thesevariable fields are decided on a “majority vote” basis across thetraining subcarriers such that decoding is possible when some of thesesubcarriers or bits are corrupted. The 16 Blocks within each Modem Frameare numbered sequentially from 0 to 15. Then the most significant bit(MSB) of the Block Count field is always set to zero since the BlockCount never exceeds 15. Modem Frame synchronization is established withknowledge of the Block Count field.

The coherent detection of this signal requires a coherent phasereference. The decoded information from the BPSK Timing Sequence is usedto remove the modulation from the training subcarriers leavinginformation about the local phase reference and noise. Referring to FIG.6, the binary (±1) timing sequence modulation is first removed from thereceived training subcarriers by multiplying them by the synchronized,decoded, and differentially-reencoded BPSK Timing Sequence. A FIR filteris used to smooth the resulting symbols over time, yielding a complexconjugated estimate of the local phase and amplitude. This value isdelayed and multiplied by an estimate of the reciprocal of the noisevariance. The noise variance is estimated by subtracting the smoothedestimate of the local phase and amplitude from the input symbols (afterappropriate time alignment), squaring and filtering the complex noisesamples, then approximating the reciprocal (with divide-by-zeroprotection). This CSI weight is interpolated over the 18 subcarriersbetween pairs of adjacent training subcarriers. The resulting local CSIweights are then used to multiply the corresponding local data-bearingsymbols.

In one embodiment, the low pass filter 158 in FIG. 6 is an 11-tap FIRfilter. The 11-tap FIR filter is used to dynamically estimate thecomplex coherent reference gain α at each reference subcarrier locationfor each symbol time. The filtering over time with the 11-tap FIRfilter, and subsequent filtering across subcarriers is performed tocompute a local estimate of the coherent reference gain α for each QPSKsymbol location over both time and frequency. A larger FIR filter withmore taps would reduce the estimation error when the signal statisticsare stationary, but the bandwidth would be too small to trackDoppler-induced changes in the signal at maximum highway speeds.Therefore 11 taps with a tapered symmetric Gaussian-like impulseresponse was considered to be appropriate. A symmetric FIR is usedinstead of an IIR filter for its linear phase property which has zerobias error for a piecewise linear (approximately) channel fadingcharacteristic over the span of the filter. This smoothed coherentreference signal output of the FIR filter is subtracted from the delayedinput samples to yield the instantaneous noise samples. These noisesamples are squared and processed by an IIR filter 174 to yield anestimate of the noise variance σ². This filter has a narrower bandwidththan the FIR filter to yield a generally more accurate estimate of thenoise variance. After appropriate sample delays to match the filterdelays, the symbol weight α*/σ² is computed for each subcarrier. Thesevalues are smoothed and interpolated across the subcarriers for eachOFDM symbol to yield more accurate estimates. This weight is unique foreach OFDM symbol and each subcarrier providing a local (time andfrequency) estimate and weight for the symbols forming the branchmetrics for a subsequent Viterbi decoder.

As used herein, the “complex coherent reference gain (α)” of a QPSKsymbol (depending on time/frequency location since it is dynamic) isdefined as α. It is a complex term, including real and imaginarycomponents, that represents the gain and phase of the symbol associatedwith it. This value is estimated by the processing and filteringdescribed. The “composite coherent channel reference signal x_(n)” isthe composite value of α computed over all the reference subcarriersover any one OFDM symbol time.

The multiple roles of the Reference Subcarriers for acquisition,tracking, estimation of channel state information (CSI) and coherentoperation have been described in the incorporated patents. The system ofU.S. Pat. No. 7,305,056 was designed to accommodate vehicles with fixedantennas. The system was designed for coherent operation in the FMbroadcast band (88-108 MHz) with fading bandwidth to accommodatevehicles at highway speeds. The various coherent tracking parameters areestimated using filters with bandwidths that approximate the maximumexpected Doppler bandwidth (roughly 13 Hz). With a fixed antenna, thepertinent tracking statistics of the input signal to the trackingalgorithms are assumed to vary at a rate no greater than the Dopplerbandwidth.

As used herein, the “complex coherent reference gain (α)” of a QPSKsymbol (depending on time/frequency location since it is dynamic) isdefined as α. It is a complex term, including real and imaginarycomponents, that represents the gain and phase of the symbol associatedwith it. This value is estimated by the processing and filteringdescribed. The “composite coherent channel reference signal x_(n)” isthe composite value of α computed over all the reference subcarriersover any one OFDM symbol time.

The third patent (U.S. Pat. No. 7,724,850) uses nonlinear filters toestimate CSI. The nonlinear filters improve performance in the presenceof impulse noise and step transients. Step transients can be caused bystepped agc or by switching antenna diversity systems. This patent islisted below, and a functional block diagram is shown in FIG. 7.

FIG. 7 shows an example wherein the 11-tap FIR filter is replaced with a5-tap median filter. The goal of the process(es) shown here is toprovide estimates of the coherent channel complex gain (“a” values)along with estimates of the noise or interference. These estimates arelocal in time and frequency (subcarrier location) to accommodate thedynamic selective fading channel experience in a mobile environment suchas a moving automobile. These estimates are derived from the referencesubcarrier symbols which have been stripped from the received anddemodulated signal as previously described, and are input on line 250 asS_(r,n) complex values. The data used to modulate these symbols isalready known and removed from these symbols with the first conjugatemultiply operation (illustrated by multiplier 252) to yield theinstantaneous complex channel gain values a2_(r,n) on line 254. Thesubsequent median filtering 256 in time reduces the noise whilemaintaining the step changes due to antenna switching to produceintermediate values a1_(r,n) on line 258. These intermediate values arefurther filtered (smoothed) over the reference subcarriers (infrequency) as shown in block 260 to produce the final complex channelgain values a_(r,n). These a_(r,n) gain values are later used outsidethis algorithm to process (equalize and provide branch metricinformation) the signal constellations for the data bearing symbols inthe conventional manner for QAM symbol demodulation.

The next step in this process is to estimate the noise associated witheach of these complex channel gain values. The instantaneous noisesamples are estimated by subtracting the a_(r,n-2) values from the(appropriately delayed) noisy corresponding input samples a2_(r,n-2), asillustrated by summation point 262. As shown in block 264, themagnitude-squared value is computed from these complex noise samples toyield the instantaneous noise variance estimates var_(n-2) on line 266.These instantaneous noise variance samples are poor estimates of thelocal (time and frequency) noise and require processing and filtering toproduce useful noise variance estimates. Although simpler time andfrequency filtering would normally be used to reduce the error of theseinstantaneous noise variance estimates, this type of filtering would noteffectively accommodate the changing noise due to fading, Automatic GainControl AGC action and step changes due to antenna switching. Thereforea median filter 268 is used to filter these instantaneous variancesamples in time to produce samples varflt_(n-16), and conventional(linear IIR or FIR filter 270) filtering is used to further smoothacross frequency (subcarriers) to produce the final variance estimatesσ_(r,n-16) in a manner similar to the complex channel gain estimatesabove. An additional feed forward path 272 is provided to capture therelatively large noise impulses that occur due to the antenna switching.When these values (scaled by a factor 0.5 as shown in block 274) exceedthe median-filtered estimate, then these larger values are selected foroutput to the frequency smoothing filter by the select max functionillustrated in block 276. These values are then smoothed over thereference subcarriers as shown in block 278. This is important insubsequent formation of the branch metrics which exploits this knowledgeof the large noise impulses.

Analyses and simulation of the algorithm improvements to the coherentreference estimation just described appear to work sufficiently well forthe cases analyzed and simulated. These cases include a flat andselective fading channel with Doppler bandwidth consistent with highwayspeeds and noise as low as 0 dB SNR. However other channel conditionsshould be considered, such as impulsive noise, or residual transienteffects not entirely suppressed by the new coherent referenceprocessing. In this case the adjusted coherent reference values of x areappropriate; however, the noise variance estimate would be corrupted.The noise impulse could be high for the symbol(s) where the impulseoccurred, but the IIR filter would suppress this noise estimate value atthe impulse instant, and spread the noise estimate over the impulseresponse time of the IIR filter. It would be preferable in this case tofeed-forward the high noise samples in parallel with the IIR path (withappropriate delay matching). For symbols where the noise pulse issufficiently higher than the IIR filter output, this noise pulse shouldbe used to determine the estimated noise variance for those symbols.When the feed-forward path is used for these noise pulses, the energyinto the IIR filter for these samples should be reduced so that thelocal noise peak is not spread over the span of the IIR filter. It iseasy to consider several variations of this process for handling noisepeaks in the noise variance estimate.

The noise variance estimation process is modified to improve performancewith switching transients and to accommodate a faster AGC. The originalnoise estimation employed a 2-pole IIR filter with parameter a= 1/16(not to be confused with the subscripted “a_(r,n)” value notations forthe complex channel gains). The peak of the impulse response of thisfilter was at a delay of 8 samples (symbols), although the decaying tailwas much longer making the step delay closer to 16 samples (symbols).

The functions described in FIGS. 6 and 7 can be performed, for example,in the digital demodulator blocks of FIGS. 1-5.

According to embodiments of the invention, these branch metrics can bemodified as described below in order to optimize their use in maximumratio combining for an FM IBOC diversity system, including adjusting fornon-linear filtering effects, warping, quantization, andsynchronization, as described in the following sections.

Analysis of Viterbi Branch Metrics

The relationship between carrier-to-noise ratio Cd/No and the VBM valuesis analyzed in this section, as this relationship influences themodifications described in subsequent sections. The VBMs are formed bymultiplying the received symbols by the computed CSIweight. Thesechannel state information (CSI) weights are derived from the referencesubcarriers and interpolated over the 18 data-bearing subcarriersbetween the neighboring pairs of reference subcarriers. This CSIweightcombines the amplitude weighting for MRC along with a phase correctionfor channel phase errors.

${CSIweight} = \frac{\alpha^{*}}{\sigma^{2}}$where a* is the complex conjugate of the estimated channel gain,relative to a quadrature phase shift keying (QPSK) symbol energy of one,and σ² is an estimate of the variance of the noise for a QPSK symbol.Since the noise variance is estimated in two dimensions for the QPSKsymbol, then σ²=No (instead of σ²=No/2 usually associated with aone-dimensional matched filter). The QPSK symbol has a nominal magnitudeof |a|=√{square root over (Es)}=√{square root over (2·Ec)}, where Es isthe energy of a QPSK symbol, and Ec is the energy of one of the two codebits of the QPSK symbol. When a received bit is multiplied by the CSIweight, it has a typical (absolute) value of

${{BM}} = {{{\sqrt{Ec} \cdot \frac{a^{*}}{\sigma^{2}}}} = {\sqrt{2} \cdot \frac{Ec}{No}}}$

The code bit energy Ec is expressed as a function of the total digitalsignal power Cd.

${Ec} = \frac{Cd}{344.53125 \cdot 191 \cdot 4}$

Then the typical (absolute) value of the branch metrics can be expressedas a function of Cd/No.

${{VBM}} = {{\frac{Cd}{No} \cdot \frac{\sqrt{2}}{{344.53125 \cdot 191}{\cdot 4}}} = {{{Cd}/{No}} - {52.7\mspace{14mu}{dB}}}}$

Adjustments for Nonlinear Filtering

The branch metric analysis described above assumes ideal linearfiltering. However, current HD Radio receiver implementations employseveral nonlinear filtering techniques to mitigate the undesirableeffects of impulsive noise and step transients due to automatic gaincontrol (AGC) and/or switched diversity antenna systems, as is describedin U.S. Pat. No. 7,724,850, which is hereby incorporated by reference.The branch metric relationship with Cd/No can be adjusted to allow forgain difference with these nonlinear filters. As shown above, thetypical branch metric relationship for the ideal linear filter model is|VBM|=Cd/No−52.7 dB

A functional block diagram of the CSI estimate technique using nonlinearfiltering is shown in FIG. 7. The top signal path in FIG. 7 shows a5-tap median filter. This filters the complex QPSK (constrained to BPSK)symbols of the reference subcarriers that have been stripped of data.The symbol values represent the complex channel gain for each referencesubcarrier. The median filter in this case does not impose a biasrelative to the weighted complex sample mean that would be obtained bylinear filtering in the case of all-white Gaussian noise (AWGN). This isbecause the two-dimensional Gaussian noise probability density functionis symmetric about the mean complex value of the QPSK symbol.

The 7-tap median filter for the noise variance estimate produces a biasrelative to a linear averaging filter. This is because the squared errorsamples have a nonsymmetric distribution about the mean. Specificallythe sum of the square of the pair of unit variance Gaussian samplesproduces a Chi-squared (σ²) distribution with 2 degrees of freedom,having a mean of 2 (2 dimensions) and a distribution of

${{{CDF}(x)} = {1 - {\mathbb{e}}^{{- x}/2}}};{{{PDF}(x)} = {\frac{1}{2} \cdot {{\mathbb{e}}^{{- x}/2}.}}}$

The variance of the noise is the mean of the Chi-squared distribution.

σ² = ∫₀^(∞)x ⋅ PDF(x)⋅ 𝕕x = 2.

The nonlinear filter in the receiver implementation approximates thevariance with the median of the Chi-squared distribution, and is solvedby

∫₀^(median)PDF(x)⋅ 𝕕x = ∫_(median)^(∞)PDF(x)⋅ 𝕕x;median = 2 ⋅ ln (1/2) ≅ 1.386.

The median value of 1.386 is relative to a linear mean of 2, yielding again of ln(2)=0.693 instead of unity gain expected of a linear filter.However, the median of a finite number of samples (e.g., 7) is biasedslightly higher than the true median of a large sample set. A simplesimulation of a sliding 7-tap median filter over 1 million Chi-squaredsamples reveals that the gain is approximately 0.76 (instead of unitygain for linear filters), underestimating the noise variance by 1.2 dB.This is due to the asymmetry of the distribution of the square of theGaussian complex samples. Then this will tend to overestimate theCSIweight by a factor of about 1.316 (1.2 dB).

There is another filter nonlinearity due to the excess short term noiseestimates. In this case large impulsive noise samples (scaled by 0.5)will be selected as the noise-squared filter output. The result is thatthe feedforward peak excess short term noise estimates will overestimatethe noise. The net result of both nonlinearities (7-tap median filter,and select max) is that the noise variance is underestimated by a factorof 0.83 (0.8 dB), so the CSIweight is overestimated by a factor of 1.2.

Simulation results of an actual receiver show the mean branch metricvalues as a function of Cd/No. The results show that the simulatedbranch metrics are a factor of 1.073 (0.3 dB error) greater than thepredicted values at typical Cd/No operating points, even aftercorrection for nonlinear filtering. One explanation why the VBMs arelarger than predicted is that the finite symbol estimation (e.g., 5-tapmedian filter) is influenced by the nonzero median of the noise overthose 5 samples. The symbol magnitude would be overestimated (althoughnot biased) at the median filter output because of the vector additionof the noise component. This would also result in underestimation of thenoise variance because the symbol median is subtracted from the othersamples, then squared to produce noise energy samples. The net errorwould be difficult to analyze because of the complication of additionalfiltering across reference subcarriers. However, this small error isassumed acceptable as sufficient verification of the filter gain foranalysis in subsequent sections.

For these reasons and according to embodiments of the inventiondescribed herein, the computed branch metric prediction for nonlinearfiltering should include an overall adjustment of about 2.3 dB(1.2+0.8+0.3 dB).|VBM|=Cd/No−52.7+2.3=Cd/No−50.4 dB

Branch Metric Warping

The ideal branch metrics increase in proportion to Cd/No. However, atlow SNR, the channel symbols become overestimated. For example, thechannel symbols estimated by the 5-tap median filter will generally havea non-zero median even when no signal is present. That is because thechannel symbol is the median of the 5 noise samples. This will cause anunderestimation of the noise variance. So, branch metrics areoverestimated (warped) at low SNR. The expression for the CSIweight canbe modified to “unwarp” the values at low SNR. This can be accomplishedby multiplying the existing CSIweight with a warp factor CSIwarp.

CSIweightw = CSIweight ⋅ CSIwarp where${CSIweight} = {{\frac{a^{*}}{\sigma^{2}}\mspace{14mu}{and}\mspace{14mu}{CSIwarp}} = \frac{1}{\left\lbrack {1 + {c \cdot \left( \frac{\sigma^{2}}{{a}^{2}} \right)^{p}}} \right\rbrack}}$

The value of parameters c and p can be empirically adjusted for bestperformance. The value of Cd/No is related to the nominal branch metricmagnitude, including the gain correction factor for the nonlinearfiltering.

${{VBM}} = {{10 \cdot {\log\left\lbrack {\frac{1}{\sqrt{2}} \cdot \frac{{a}^{2}}{\sigma^{2}}} \right\rbrack}} = {{{Cd}/{No}} - {50.4\mspace{14mu}{dB}}}}$${{Cd}\text{/}{No}} = {{10 \cdot {\log\left\lbrack {\frac{1}{\sqrt{2}} \cdot \frac{{a}^{2}}{\sigma^{2}}} \right\rbrack}} + 50.4}$

The plots of FIG. 8 show the effects of CSIwarp over a range of Cd/No,that is, the suppression of branch metrics at low SNR. Simulationresults suggest using c=0.25, p=2, since it tends to offer the bestperformance over various conditions. As used in this description, “lowSNR” means near zero dB (Ec/No) or lower.

Branch Metric Quantization

Memory constraints are satisfied by imposing quantization on the branchmetrics. Quantization is determined by the number of bits used torepresent the VBMs. Although 8 bits of quantization have been used, itis desirable to reduce this to fewer (e.g., 4) bits. The optimalquantization zone width (quantization resolution) is defined by thefollowing formula:

$T = \sqrt{\frac{No}{2^{b}}}$where No is a noise power spectral density, b is the number of bits fora soft decision, and T is in units of √{square root over (Ec)}. So atEc/No=1, the quantized value of the branch metric should be √{squareroot over (2^(b))}. The computed VBM in an IBOC receiver already has afactor of √{square root over (2)} in the computation, as well as afactor of about 1.3 due to the nonlinear filtering gain.

${{VBM}} = {{{\sqrt{Ec} \cdot \frac{{\hat{a}}^{*}}{\sigma^{2}}}} = {1.3 \cdot \sqrt{2} \cdot \frac{Ec}{No}}}$

Then the practical scale factor for the IBOC receiver branch metricsshould be:scale=0.544·√{square root over (2^(b))}Branchmetric_(—)nzq=max{−2^(b-1)+1,min{2^(b-1)−1,round[scale·Branchmetric_(—) nz]}}.

In one example, for b=4 bits of quantization, the scale factor could bescale=2.17. So ±4 would represent the quantized values at Ec/No=1, aboutCd/No=54.2 dB_Hz. The maximum range is +7/−8, about 3 dB greater than±Ec/No.

FIG. 9 is a diagram showing scaling (scale=2.17) and quantization forViterbi Branch Metrics. In FIG. 9, the numbers are the actual integerquanta values represented with 4 bits (16 possible numbers in 2'scomplement). For this example, an integer value of 4 (or ±4) isequivalent to Ec/No=1, or zero dB, where Ec/No is the code bit energydivided by the noise density.

The combined effects of scaling, quantization and warping were simulatedto empirically determine the parameter settings for warping (p and c) aswell as the scale factor associated with VBM quantization bits. Thesesimulation results suggest a different scale factor than the previousanalysis. Table 1 shows the recommended scale values for variousquantization choices (bits for VBM).

The benefits of warping are best measured with one sideband, since thewarping mitigates contamination from the missing sideband due to nonzero(noisy) VBMs. VBM quantization with best scaling was simulated (exceptan additional VBM scale factor of 32 was also used for 8-bitquantization to ensure saturation in the case of high impulsive noisesamples). The recommended warping parameters are c=0.25, p=2. Over allconditions simulated, for 4-bit quantization, the loss is less than halfa dB. For 3-bit quantization, it is less than one dB (with warping). For2-bit quantization, degradation is less than 2 dB (again, with warping).The best choices for scale factor for each VBM quantization (bits) arebolded in Table 1.

TABLE 1 VBM Quantization Loss with Measured Best Scaling, BER Results ofMatlab FM Simulation Warping, c = 0.25, p = 2, Seed = 100, 5/24-25/12BER Degrad. (dB) vs. BER Degrad. (dB) vs. VBM Floating-Point VBMs, BERDegrad. (dB) vs. Floating-Point VBMs, Quantization VBM AWGN @ 56 dB-Hzwith Floating-Point VBMs, UF Rayleigh Fading (bits) Scaling Warping OneSideband Disabled AWGN @ 54 dB-Hz @ 57 dB-Hz Float NA OFF — — — Float NAON −0.3 0.05 0.05 8 32 OFF 0.05 0.01 0 8 32 ON −0.05 0.08 0.12 8 8.704OFF −0.15 0.06 0.04 8 8.704 ON −0.3 0.07 0.12 4 3.5 OFF 0.48 0.07 0.33 43.5 ON 0.17 0.11 0.34 3 2.5 OFF 1.11 0.3 0.71 3 2.5 ON 0.76 0.31 0.79 22 OFF 2.24 0.82 1.75 2 2 ON 1.22 0.85 1.68

Synchronization of VBMs

In the disclosed embodiments, both of the first and second receiversignal paths may operate independently (asynchronously). The VBMs fromeach receiver path are combined when available. Both receiver paths usetheir own acquisition and tracking, and the branch metrics must bealigned for combining. When only one receiver path has valid branchmetrics, then the branch metrics from the other receiver path are notadded.

Performance is near optimum when both receiver paths are tracking thesignal with proper synchronization. The main performance enhancement isachieved in dynamic fading conditions. When one antenna is in a deepfade, the other antenna may not be faded, and vice versa. Tracking canflywheel over short fades or outages.

When one of the receiver paths is not tracking the signal, its branchmetrics are effectively zero and MRC offers no additional advantage tothe tracking demodulator, except to improve the probability that atleast one demodulator is decoding the signal. This situation could beimproved if tracking information were shared between receivers. The lossmay be apparent in AWGN where tracking can be lost due to operationbelow the single-receiver SNR threshold, where the combining gain wouldoffer sufficient bit error rate (BER) performance if this receiver wastracking.

Alternatively, both receiver paths could share synchronization based onboth antenna signals. This option offers better performance, butextensive demodulator software modifications are required over thesingle demodulator. Alignment between branch metrics is trivial becauseboth receiver paths are already synchronized. The acquisition andtracking is common to both signal paths. Synchronization between thepair of input signal paths should be ensured, and tuner local oscillatorfrequencies should be locked. Performance is improved under allconditions. The acquisition and tracking performance is improved alongwith the signal decoding BER performance.

II. Acquisition and Frame Synchronization Using DSQM

As previously stated, an FM IBOC receiver that implements MRC operatesat low SNR conditions. Existing IBOC receivers use parameters foracquisition and frame synchronization that can, according to embodimentsof the invention described herein, be optimized for these low SNRconditions using a Digital Signal Quality Metric (DSQM).

The Digital Signal Quality Metric (DSQM) is an algorithmic function usedto measure (compute) the quality of a digital OFDM signal. The DSQM is anumber ranging from zero to one, indicating the viability of the digitalsidebands of an FM IBOC signal. A value near zero indicates that nouseful signal is detected, while a value near one indicates that thesignal quality is nearly ideal. A midrange value of 0.5, for example,indicates a corrupted but possibly decodable digital signal. U.S. Pat.No. 7,933,368 describes the DSQM function, and is hereby incorporated byreference.

The DSQM has several applications: 1) detect a viable digital signalchannel for digital seek/scan, 2) establish initial symbolsynchronization and carrier frequency offset for digital signalacquisition, 3) assess antenna element signal quality for diversityswitching and MRC, where a more-efficient version, DSQM-lite, exploitsknowledge of existing symbol synchronization.

FIG. 10 is a functional block diagram of DSQM processing. Upper sidebandand lower sideband signals are received on lines 300 and 302respectively. These signals can be received from sideband isolationfilters at 186 ksps (where decimation by 2 filters are used for 372ksps). The signals are shifted to base band in mixers 304 and 306.Preacquistion filters 308 and 310 filter the baseband signals. Signalquality metrics Q and peak index P for each digital sideband aredetermined as shown in blocks 312 and 314. Then the combined qualitymetrics Q and peak index P are used to compute a DSQM as shown in block316. An estimate of symbol timing and (sub)carrier frequency offset forthe initial acquisition case is computed as shown in block 318.

The DSQM computation shown in FIG. 10 is comprised of 5 relatedcomponents: 1) shift center frequency of the preacquisition signalbandwidth to baseband, 2) preacquisition filter each sideband, 3)compute signal quality metrics Q and peak index P for each digitalsideband, 4) combine the signal quality metrics to form composite DSQM,and 5) estimate symbol timing and (sub)carrier frequency offset for theinitial acquisition case.

A portion of the USB and LSB signal bandwidths is used for the DSQMestimation. In one example, the desirable frequency portion is centeredat about 155 kHz for the USB, and ˜155 kHz for the LSB. A bandwidth ofabout 46.5 kHz is useful for DSQM because it allows for suppression of apotential first-adjacent analog signal. Nyquist sampling of thesesignals results in efficient computation.

The DSQM also estimates receiver symbol boundary and frequency errorcaused by different transmitter and receiver reference oscillators andsymbol boundary uncertainty. Its one-time corrections are applied priorto the start of demodulation; synchronization is maintained thereafterby tracking control in the demodulator.

A more detailed description of DSQM is provided below, in Section III.DSQM Algorithm Description. A more efficient implementation of DSQM,called DSQM-lite, can be used for antenna diversity switching. U.S.patent application Ser. No. 13/165,325, filed Jun. 21, 2011 and titled“Method And Apparatus For Implementing Signal Quality Metrics AndAntenna Diversity Switching Control”, describes the DSQM-lite function,and is hereby incorporated by reference. The efficiency of DSQM-lite isderived from knowledge of the symbol synchronization after the signalhas been acquired. Instead of processing the entire symbol vector, theDSQM is computed only for the synchronized samples within the symbol.

DSQM and/or DSQM-lite can be used to optimize parameters for the use ofMRC antenna diversity in a receiver operating at a lower SNR. Sinceperformance in AWGN can improve as much as 3 dB, the acquisition andtracking should also be capable of operating 3 dB lower. Even greaterimprovements in reception sensitivity are possible in fading. However,the fourth-power symbol tracking in the previously used demodulatorimplementations breaks down at these lower SNR operating conditions.Thresholds on DSQM and correlation requirements with sync patterns inthe reference subcarriers for frame sync could be modified to improveacquisition at lower SNR. A functional block diagram of a receiveremploying the MRC antenna diversity technique for OFDM signals is shownin FIG. 1.

A signal processing strategy described below includes eliminating thefourth-power symbol tracking, along with the fourth-power “Badtrack”detection. Badtrack is a condition where the symbol tracking settlessomewhere other than the actual symbol boundary, and remains stuckthere. The fourth-power technique is commonly used to strip the dataphase modulation imposed upon QPSK symbols. This leaves the complex gaininformation used to estimate Channel State Information (CSI) that isused in subsequent Viterbi Branch Metric computations. The fourth-poweroperation multiplies the angle of the complex gain by 4. This isremedied by dividing the resulting angle by 4 to yield the channelphase. However, it also multiplies the noise by a factor of 4. This istypically acceptable for operation of a single receiver, since theacquisition and tracking algorithm based on the fourth-power operateacceptably at the lowest SNR for useful data. However, the loweroperating SNR of an MRC receiver is prevented because of the increasednoise due to fourth-power processing, so an alternate technique issought.

Since the fourth-power processing is discarded, the symbol tracking isleft to flywheel using the symbol timing sample offset determined byDSQM during this period. The sample timing error will drift during thistime due to clock error (e.g., 100 ppm results in 18.6 samples/sec driftat 186 kHz sample rate). If the symbol timing drifts too far, then thesymbol tracking loop may not be able to converge to the correctoperating point. The symbol tracking using reference subcarriers isstarted after an initial subframe is found, which will prevent furthersymbol timing drift. Therefore, to avoid a false track condition, areacquisition should be invoked within about 0.5 seconds after DSQM ifthe initial subframe is not found.

It is important to suppress faulty branch metrics from a demodulator sothat it does not contaminate the alternate demodulator. This can happenduring a faulty symbol tracking condition at low SNR. It is notnecessarily a problem with a single (non MRC) demodulator because thesignal may be undecodable anyway. Since MRC combines branch metrics fromboth demodulators, the possibility of contamination should be avoided. ADSQM-based Badtrack detector is described below for this purpose, aswell as for reacquisition.

In addition, filtering should be used as described in the followingsections.

Preacquisition Filtering

To prevent falsely acquiring on large second-adjacent channels, eachprimary sideband can be filtered prior to DSQM processing. Thepre-acquisition filter can be designed to provide 60-dB stopbandrejection while limiting the impact on the desired primary sideband.

An efficient means of computing the DSQM involves decimating the inputcomplex baseband signal sample rate to approximately 46.5 ksps for eachdigital sideband (LSB & USB). This can be accomplished by using the setof isolation filters. However, if the output sample rate of the digitalsidebands is 372 ksps, then a pair of decimation-by-2 filters can beinserted in front of the complex mixers and preacquisition filters toprovide the expected sample rate of 186 ksps.

Halfband Highpass Filter

FIG. 11 is a functional block diagram of preacquisition filters precededwith decimation filters. FIG. 11 shows the complex mixers 320, 322 andpreacquisition filters 324, 326 proceeded by a Halfband Highpass filter328, 330 to reduce the input sample rate from 372 to 186 ksps. ComplexUSB and LSB baseband digital samples are output from the USB and LSBisolation filters at 372 ksps. A Halfband Highpass filter is used todecimate the USB or LSB sample rates from 372 ksps to 186 ksps. Thespectrum of this filter has halfband symmetry, with alternatingcoefficients equal to zero. Integer versions of these filtercoefficients are presented in Table 2, showing only one-sidedcoefficients starting at center coefficient index 0 through 15. Theseinteger coefficients would be multiplied by 2⁻¹⁵ for a unity passbandgain. The negative-indexed coefficients (not shown in Table 2) are equalto the positive-indexed coefficients.

After decimation-by-2 to 186 ksps, and complex mixing, the USB and LSBdigital sidebands undergo further filtering by the pre-acquisitionfilter. This filter should have linear phase and a minimum output samplerate consistent with passband characteristics. The upper and lowersidebands should each have a passband of about 46 kHz, in order tominimize corruption from first-adjacent analog and second-adjacentdigital interference. This filter can be designed using a decimate-by-4output sample rate (46.51171875 ksps).

TABLE 2 Positive-Indexed Coefficients of Halfband Highpass USB or LSBFilter. Coefficients 0 through 15 of Halfband Filter, Starting withCenter Coefficient 0 16384 4 0 8 0 2 0 1 −10292 5 −1479 9 −343 3 −34 2 06 0 10 0 4 0 3 3080 7 741 11 131 5 4

FIG. 12 shows the spectrum of Highpass Halfband Filter beforedecimation-by-2. The output after decimation-by-2 will center the filterpassband to zero Hz. The plots show the undecimated responses over theNyquist bandwidth for complex input sample rate 372 ksps, although onlythe decimated output is computed (for efficiency). Notice that thebaseband 6-dB passband spans the halfband bandwidth from 93 kHz to 279kHz, the Nyquist bandwidth at the output sample rate. The LSB decimationfilter has an identical spectrum, but with negative frequencies. In FIG.12, the units for the vertical axis are dB and for the horizontal axisHz (frequency); k is a sample index, and K is the total number ofsamples in FFT.

Quarterband Pre-Acquisition Filter

The quarterband pre-acquisition filter efficiently isolates a portion ofthe output passband of the upper or lower primary digital sidebandfilter, suppressing the effects of adjacent-channel interference. In oneembodiment, prior to filtering, the isolated USB is effectivelyfrequency-shifted by −155.0390625 kHz, and the isolated LSB iseffectively frequency-shifted by +155.0390625 kHz. The frequencyshifting centers the pre-acquisition filter at baseband (dc), reducingcomplexity by allowing a symmetric (real) quarterband filter. Inpractice, the frequency shifting can be accomplished by mixing thebaseband alias of the input USB by 31.0078125 kHz (e^(j·π·n/3)). In asimilar manner, the baseband alias of the input LSB can be shifted by−31.0078125 kHz (e^(−j·π·n/3)). This frequency shifting allows thecomplex phasor to be stored in a circular lookup table with only 6coefficients per cycle.

In one example, vectors for complex frequency shifting and filtercoefficients are computed and pre-stored. Pre-store the complexexponential in a 6-element vector fshft.

${fshft} = {\begin{pmatrix}1 \\{\exp\left\{ {j \cdot {\pi/3}} \right\}} \\{\exp\left\{ {j \cdot 2 \cdot {\pi/3}} \right\}} \\{- 1} \\{\exp\left\{ {{- j} \cdot 2 \cdot {\pi/3}} \right\}} \\{\exp\left\{ {{- j} \cdot {\pi/3}} \right\}}\end{pmatrix} = \begin{pmatrix}1 \\{0.5 + {j \cdot 0.866}} \\{{- 0.5} + {j \cdot 0.866}} \\{- 1} \\{{- 0.5} + {j \cdot 0.866}} \\{0.5 - {j \cdot 0.866}}\end{pmatrix}}$

The pre-acquisition filter output is further decimated by 4, and issubsequently used for acquisition. The filter spectrum has quarterbandsymmetry, in which every fourth coefficient is zero. Integer versions ofthese filter coefficients are presented in Table 3, showing onlypositive-indexed coefficients, starting at center index 0 through 11.These integer coefficients would be multiplied by 2⁻¹⁵ for unitypassband gain. The negative-indexed coefficients are equal to thepositive-indexed coefficients.

TABLE 3 Positive-Indexed Coefficients of Quarterband Pre-acquisitionFilter Coefficients 0 through 11 of Quarterband Pre-acquisition Filter,Starting with Center Coefficient 0 8192 1 7242 2 4846 3 2080 4 0 5 −9126 −852 7 −386 8 0 9 130 10 100 11 40

The magnitude spectrum of one embodiment of the pre-acquisition filterfor the USB is shown in FIG. 13. The plots show the responses over aselected bandwidth within the 372 ksps sample rate so the filter effectsbeyond 200 kHz can be seen on the plot. The actual output of thepreacquisition filter is aliased to center the filter at zero Hz at asample rate of 46.5 ksps. These plots include the output spectrum of theupper primary digital sideband decimation filter, and the effectivespectrum of the quarterband pre-acquisition filter. Notice that thebaseband passband spans the quarterband bandwidth from about 132 to 178kHz. This passband was chosen to minimize corruption during acquisitiondue to first-adjacent analog FM interference and second-adjacent digitalsideband interference. The LSB characteristics are the same, but withnegative baseband frequencies.

III. DSQM Algorithm Description

The DSQM computation exploits cyclic prefix correlation within eachsymbol to construct correlation peaks. The position of the peaksindicates the location of the true symbol boundary within the inputsamples, while the phase of the peaks is used to derive the frequencyoffset error over a subcarrier spacing. Frequency diversity is achievedby independently processing the upper and lower primary sidebands. Whenboth sidebands are viable, then they are combined to improve theestimate. An efficient means for computing the DSQM involves decimatingthe frequency-shifted input complex baseband signal sample rate toapproximately 46.5 ksps. A functional block diagram of an embodiment ofthe quality metric computation for each sideband is shown in FIG. 14.

FIG. 14 illustrates the USB or LSB quality metric computations. Theinputs to DSQM Processing are symbol-size blocks of upper and lowerprimary sideband samples. Each block is comprised of 135 complex samplesat a rate of approximately 46.5 ksps, representing one symbol time.These blocks have arbitrary boundaries that do not necessarily coincidewith the boundaries of the transmitted symbols. However, by exploiting acorrelation inherent within the transmitted symbols, their trueboundaries can be ascertained.

The input 340 is a 135-sample symbol received from either the upper orlower sideband preacquisition filter. The input samples are shifted by128 samples 342 and the complex conjugate 344 of the shifted samples ismultiplied 346 by the input samples. Sixteen symbols are folded as shownby block 348 and adder 350. The folded sums are filtered by a matchedfilter 352.

The magnitude squared 354 of each input symbol is delayed 342 by 128samples and added 356 to the current magnitude-squared samples 358.Sixteen symbols are folded as shown by block 360 and adder 362. Thefolded sums are matched filtered 364. The ratio of the square of theabsolute value of the output of matched filter 352 and the square of theoutput of the matched filter 364 is computed as show in block 366 toproduce signal Q_(m). The index of the peak value of Q is found as shownin block 368. The complex peak value is picked and normalized as shownin block 370, and the result is used for frequency offset estimation.

In the example illustrated by FIG. 14, due to a cyclic prefix applied atthe transmitter, the first and last 6 samples (at 46.5 ksps) of eachtransmitted symbol are highly correlated. It is assumed that azero-value sample is synchronized to the symbol boundary, so processingof the seventh sample is avoided. DSQM processing reveals thiscorrelation by complex-conjugate multiplying each sample in itsarbitrary symbol framing with its predecessor 128 samples away. When theproducts lie within the cyclic prefix region of the same transmittedsymbol, they form a 6-sample peak with a common phase and amplitude thatreflects half of the complementary root-raised-cosine pulse shape oneach end of the symbol. The location of this correlation peak within the135-sample product indicates the transmitted symbol boundary, and thephase indicates the frequency error.

The 6-sample correlation peak over a single symbol is not easilydistinguished from the noisy products of the uncorrelated samples. Toenhance detectability of the peak, the corresponding correlationproducts of 16 contiguous symbols are “folded” on top of one another(pointwise added) to form a 135-sample acquisition vector. This“conjugate-fold” operation, after initializing vector u to zeroes, isdescribed asu _(mod(n,135)) =u _(mod(n,135)) +y _(n) ·y* _(n-128); for n=0, 1, . . ., 135·S−1,or equivalently,

${{u_{m} = {\sum\limits_{s = 0}^{S - 1}\;{y_{m + {135\; s}} \cdot y_{m - 128 + {135\; s}}^{*}}}};{{{for}\mspace{14mu} m} = 0}},1,\ldots\mspace{14mu},134,$where y is the input signal from the preacquisition filter, u is thefolded acquisition vector, m is the folded vector sample index, s is thefolded symbol index, and S=16 is the acquisition block size (or totalnumber of folded symbols).

The 6-sample folded peak, although visible within the acquisitionvector, is still somewhat noisy. Therefore, the peak is enhanced with a6-tap FIR filter h_(k) whose impulse response is matched to the shape ofthe correlation peak.

${w_{m} = {\sum\limits_{k = 0}^{5}\;{u_{{mod}{({{m + k},135})}} \cdot h_{k}}}};$for  m = 0, 1, …  , 134where m is the output sample index, u is the matched-filter input, w isthe matched filter output, and h the filter impulse response definedbelow.

${h_{k} = {\cos\left( {\pi \cdot \frac{\left( {{2 \cdot k} - 5} \right)}{14}} \right)}};$${{{or}\mspace{11mu} h} = {{\begin{pmatrix}0.434 \\0.782 \\0.975 \\0.975 \\0.782 \\0.434\end{pmatrix}\mspace{20mu}{for}\mspace{14mu} k} = 0}},1,\ldots\mspace{14mu},5$

Notice that this filter is even symmetric with 6 taps, having aneffective group delay of 2.5 samples. This group delay must beaccommodated when locating the symbol-synchronized samples at the highernon-decimated sample rate.

The correlation peak is enhanced by normalization. Not only is there aphase correlation between the first and last 6 samples of an OFDMsymbol, but there is also an amplitude correlation due to theroot-raised cosine pulse shaping applied at the transmitter. Thisamplitude correlation can be exploited as follows. The magnitude squaredof each input symbol is delayed by 128 samples and added to the currentmagnitude-squared samples, as shown in FIG. 14. After folding the first16 symbols and matched filtering, a symbol boundary is apparent. Thelocation of the symbol boundary is marked by a reduction in amplitude ofthe resultant waveform. Normalization of the existing correlation peakwith this waveform enhances the peak by reducing the level of allsamples except those coincident with the symbol boundary. Thisoperation, after initializing vector v to zeroes, is described asv _(mod(n,135)) =v _(mod(n,135)) +|y _(n)|² +|y _(n-128)|²; for n=0, 1,. . . , 135·S−1,or equivalently,

${v_{m} = {\sum\limits_{s = 0}^{S - 1}\left( {{y_{m + {135\; s}}\; }^{2} + {y_{m - 128 + {135\; s}}}^{2}} \right)}};$for  m = 0, 1, …  , 134,

where y is the input signal from the preacquisition filter, v is thefolded vector, m is the folded vector sample index, s is the foldedsymbol index, and S=16 is the acquisition block size (or total number offolded symbols).

The 6-sample folded peak, although visible within the acquisitionvector, is still somewhat noisy. Therefore, the vector v is enhancedwith a 6-tap FIR filter g_(k) whose impulse response is matched to theshape of the symbol boundary region.

${x_{m} = {\sum\limits_{k = 0}^{5}\;{v_{{mod}{({{m + k},135})}} \cdot g_{k}}}};$for  m = 0, 1, …  , 134.

The matched filtering of the normalization waveform is identical to thatperformed for the correlation peak, except the matched filter taps aresquared and then halved to ensure proper normalization:

$\begin{matrix}{g_{k} = h_{k}^{2}} \\{{{for}\mspace{14mu} k} = {0,1\ldots\mspace{11mu},5}}\end{matrix};{{{or}\mspace{14mu} g} = \begin{pmatrix}0.094 \\0.306 \\0.475 \\0.475 \\0.306 \\0.094\end{pmatrix}}$where k is the index of taps in the matched filters, h_(k) are theexisting taps for the conjugate-multiplied correlation peak, and g_(k)are the new taps for the normalization waveform. Notice that this filteris also even symmetric with 6 taps, having an effective group delay of2.5 samples. This group delay must be accommodated when locating thesymbol-synchronized samples at the higher non-decimated sample rate. Aquality metric vector Q is computed from vectors w and x.

${{Q_{m} = \frac{{w_{m}}^{2}}{x_{m}^{2}}};{{{for}\mspace{14mu} m} = 0}},\ldots,134$

The peak value Q_(P) of the vector Q, and its index P, are identified.The peak value Q_(P) is further processed to reduce the probability offalse detection due to a spur, for example. A strong spur in the absenceof noise or digital signal could produce a correlation peak that isgreater than one over the entire symbol correlation vector. To preventthis false detection, conditions are placed on the Q_(P) result, whichwould zero the Q_(P) if a false detection is suspected. One condition isthat the peak Q_(P) value must be less than one. A second condition isthat the sum of the correlation samples, spaced every 3 samples awayfrom the peak sample, must be less than some value (for example, thissum must be less than 2). This discrimination is implemented bymultiplication of the peak value Q_(P) by two Boolean (0 or 1 value)expressions.

$Q_{P} = {Q_{P} \cdot \left( {Q_{P} < 1} \right) \cdot \left( {{\sum\limits_{k = 1}^{44}\; Q_{{mod}{\{{{P + {3 \cdot k}},135}\}}}} < 2} \right)}$

The peak value of the normalized correlation waveform is representativeof the relative quality of that sideband. The entire computation justdescribed in this section is done for both the USB and the LSB, and thefinal results are saved as Q_(U), Q_(L), P_(U) and P_(L) for subsequentDSQM computation.

Once the correlation waveform is effectively normalized for eachsideband, the value and index of the peak are found. The peak indexdelta compares the peak indices of the upper and lower sidebands foreach sixteen-symbol block. Since the symbol boundaries are modulo-135values, the computed deltas must be appropriately wrapped to ensure thatthe minimum difference is used.ΔP=min{|P _(U) −P _(L)|135−|P _(U) −P _(L)|}where P_(U) and P_(L) are the peak indices of the normalized correlationwaveform for the upper and lower sidebands.

DSQM Calculation

Once the peak index delta and quality estimates have been computed, theyare used to calculate the DSQM. The DSQM separately examines the qualityof each individual sideband, in addition to evaluating the peak indexdelta and sum of the quality estimates from both sidebands. In this way,a viable signal can be successfully identified even when one of itssidebands has been corrupted by interference.

False detections may occur on an analog-only signal in a very low-noisechannel. In this case, some of the FM signal components exist in theDSQM detection band, and can trigger DSQM detection. The correlation onupper and lower sidebands is unlikely to peak at the same location, andthis false detection would more likely occur on one sideband only.

A temporal consistency check can be used to discriminate against thiscondition. This temporal consistency check prevents initial detection onone sideband only. If only one sideband passes the threshold on thefirst DSQM measurement, and ΔP>1, then a second DSQM computation is usedto assess if the correlation peak occurs at the same location (P_(L), orP_(U)) on that sideband. If the peak index from a sideband is consistenton two consecutive DSQM measurements, then the acquisition is declaredsuccessful.

The flowchart of FIG. 15 can be used for acquisition of the digitalsignal. It can also be used in a seek function, coordinated by the hostcontroller, for example. The seek signal quality threshold SeekThres isusually set to a higher level than that used for acquisition, so thatthe seek function stops on only a reasonably good signal. The normalacquisition threshold Thres is lower to allow acquisition on marginalsignals. Seek or acquisition is determined to be successful or not afterone or two iterations. The algorithm continues to iterate until thedigital signal is successfully acquired, or is interrupted by the hostcontroller, for example.

The first iteration of the ACQ algorithm 380 is indicated byinitializing the InitFlag to one, and DSQMSeqNum to one (block 382).Quality metrics Q_(L) and Q_(U), peak index indices P_(L) and P_(U), andΔP are computed (block 384). If the initial flag is not equal to 1(block 386), a Temporal Consistency Check is performed on each sideband(block 388), except on the first iteration when previous Peak indicesare not available. If the initial flag is equal to 1, a DSQM is computedand selected (maximum Q, if ΔP<2); upper and/or lower sideband(s) areidentified by setting L_(acq)=1 and/or U_(acq)=1 (block 390). If thisDSQM value exceeds the acquisition threshold Thres (e.g., Thres=0.2)(block 392), then the DSQM value, along with DSQMSeqNum and DSQMDetBit,are output (block 394). The DSQMDetBit is determined by Boolean resultof comparing the DSQM to the Seek Threshold (e.g., 0.5).DSQMDetBit=DSQM>SeekThres

If the first DSQM (of this iteration) fails to exceed the acquisitionthreshold (e.g., 0.2), then another DSQM is computed based on themaximum of Q_(L) or Q_(U) (but not both together) (block 396). If thisDSQM fails to exceed the acquisition threshold (block 398), then thisDSQM value, DSQMSeqNum and DSQMDetBit are output (block 400) andDSQMSeqNum is incremented (block 402); the next iteration of thealgorithm is then executed using the parameters in block 403. However,if this DSQM exceeds the acquisition threshold, then successfulacquisition is declared (block 404) (if this is not the first algorithmiteration, block 406); otherwise, the next algorithm iteration canresume.

IV. Frequency & Timing Acquisition Example

Acquisition is the process of establishing initial symbolsynchronization and frequency offset for subsequent tracking. Athreshold for DSQM is established where a sufficiently reliable signalis detected. The symbol timing sample is determined by the peak qualityindex P. This index is determined with a decision rule based on whichsidebands were used to yield the final DSQM value. The selectedsidebands are indicated by the Boolean values of Lacq and Uacq, asdetermined in the algorithm of FIG. 15. If either the USB or LSB alonewere used, then the peak index would be the index of the selectedsideband. However, if both sidebands were used, then the indices areaveraged modulo 135. Adjustments to this value for decimation, filterdelays, or other implementation delays must be performed.

$P = \left\{ \begin{matrix}P_{L} & {;{{if}\mspace{14mu}{\left( {{Lacq} = 1} \right)\hat{}\left( {{Uacq} = 0} \right)}}} \\P_{U} & {;{{if}\mspace{14mu}{\left( {{Lacq} = 0} \right)\hat{}\left( {{Uacq} = 1} \right)}}} \\\frac{P_{L} + P_{U}}{2} & {;{{if}\mspace{14mu}{\left( {{Lacq} = 1} \right)\hat{}{\left( {{Uacq} = 1} \right)\hat{}\left( {{{P_{L} - P_{U}}} < 2} \right)}}}} \\134.5 & {;{{if}\mspace{11mu}{\left( {{Lacq} = 1} \right)\hat{}{\left( {{Uacq} = 1} \right)\hat{}\left( {{{P_{L} - P_{U}}} > 133} \right)}}}}\end{matrix} \right.$

The frequency offset in Hz can be estimated using the complex value ofthe normalized correlation peak. The value for each sideband can bephase-adjusted to accommodate the frequency-shifting from the center ofthe preacquisition bandwidth. The final value depends on whichsideband(s) is used, per the following expression:

${Qcmplx}_{U} = {\frac{{w\_ upper}_{P_{U}}}{{x\_ upper}_{P_{U}}} \cdot {\mathbb{e}}^{j \cdot 2 \cdot {\pi/3}}}$${Qcmplx}_{L} = {\frac{{w\_ lower}_{P_{L}}}{{x\_ lower}_{P_{L}}} \cdot {\mathbb{e}}^{{{- j} \cdot 2 \cdot \pi}\text{/}3}}$${Qcmplx} = \left\{ \begin{matrix}{Qcmplx}_{U} & {;{{if}\mspace{14mu}{\left( {{Uacq} = 1} \right)\hat{}\left( {{Lacq} = 0} \right)}}} \\{Qcmplx}_{L} & {;{{if}\mspace{14mu}{\left( {{Uacq} = 0} \right)\hat{}\left( {{Lacq} = 1} \right)}}} \\{{Qcmplx}_{U} + {Qcmplx}_{L}} & {;{{if}\mspace{14mu}{\left( {{Uacq} = 1} \right)\hat{}\left( {{Lacq} = 1} \right)}}}\end{matrix} \right.$

The frequency error in Hz is proportional to the angle of Qcmplx.

$f_{error} = {{\frac{f_{subcarrier\_ space}}{2 \cdot \pi} \cdot \arctan}\mspace{11mu}\left\{ \frac{{Im}\;({Qcmplx})}{{Re}({Qcmplx})} \right\}}$

However the NCO may require the negative of this frequency error to betranslated into a phase increment phinc in radians per sample.

${{phinc} = {- \frac{2 \cdot \pi \cdot f_{error}}{f_{s}}}};$where f_(s) is the NCO sample rate.

Furthermore, it is common for fixed-point implementations to use themodulus range of a two's complement number to represent a full circle.

V. DSQM-Lite for Antenna Diversity

While a digital signal quality metric (DSQM) can be used for antennadiversity switching, the DSQM computed during signal acquisition iscomputationally intensive, and involves redundant processing aftersymbol synchronization is established. This section describes analgorithm for more efficient DSQM computation, called DSQM-Lite. It isderived from the acquisition algorithm described in previous sections,but the computational complexity is reduced by taking advantage ofsymbol synchronization. Since the locations of the cyclic prefix regionsof the symbols are known, there is no need to compute all thecorrelation points across the entire symbol.

This DSQM function is based on the previously described DSQM techniqueto generate an appropriate metric that can be used for antenna diversityswitching (among other uses). The DSQM algorithms process groups of 16symbols to produce a metric.

Since the symbol boundaries are already established in the symboldispenser when the DSQM is used for diversity switching, there is noneed to compute more than one peak, and the phase information is notneeded or used here.

Efficient Computation of DSQM for Diversity Switching

After initial acquisition as described in Section IV above, asubstantial reduction in MIPS (millions of instructions per second) canbe realized by limiting the processing of signal samples to the cyclicprefix regions of the symbols. Since the symbol samples are alreadyframed by the symbol dispenser in the present implementation, it isrelatively straightforward to select the cyclic prefix regions for DSQMprocessing. There are only 6 samples to process at each end of the135-sample symbol at the decimate-by-16 sample rate. It will be shownlater that only sample indices 1 through 6 and 129 through 134 need tobe computed; sample 0 is not needed since it should be synchronized tohave a zero value.

DSQM-Lite Computation

A process for computing DSQM-Lite uses the following steps.

STEP 0 (for 372 ksps input): If the input sample rate is notapproximately 186 ksps, then a decimation filter can be inserted toachieve that sample rate. A Halfband Highpass decimation filter waspreviously described for this purpose; however, it is more efficient tocompute only the samples needed for this DSQM-lite computation. DefineUSB2x and LSB2x as the 1080-sample input symbol vectors at 372 ksps.These vectors are filtered by the 31-element Halfband Highpass filterhbf, while decimating by 2 to yield 540-element vectors USB and LSB.Notice that although 540-sample vectors are generated, only the rangen=1 to 35 and n=505 to 539 need be computed, and the remaininguncomputed elements are set to zero.

${{USB}_{n} = {\sum\limits_{k = 0}^{30}\;{{USB}\; 2{x_{{2 \cdot n} + k} \cdot {hbf}_{k}}}}};$for n = 1  …  35  and   n = 505…  539${{LSB}_{n} = {\sum\limits_{k = 0}^{30}\;{{LSB}\; 2{x_{{2 \cdot n} + k} \cdot {hbf}_{k}}}}};$for n = 1  …  35 and n = 505  …  539

Uncomputed elements n=0 and n=36 through 504 are not used in subsequentcalculations. Filter coefficients for hbf are scaled by 2⁻¹⁵ for fixedpoint implementation.

${hbf} = \begin{pmatrix}4 \\0 \\{- 34} \\0 \\131 \\0 \\{- 343} \\0 \\741 \\0 \\{- 1479} \\0 \\3080 \\0 \\{- 10292} \\16384 \\{- 10292} \\0 \\3080 \\0 \\{- 1479} \\0 \\741 \\0 \\{- 343} \\0 \\131 \\0 \\{- 34} \\0 \\4\end{pmatrix}$

STEP 1: Place the frequency-shifted endpoints pshft and qshft for theupper and lower sidebands in vectors for each symbol:

${pshft\_ upper}_{n} = \left\{ {{\begin{matrix}{{{USB}_{n - 7} \cdot {fshft}_{{mod}{({n + {5,6}})}}};{{{for}\mspace{14mu} n} > 7}} \\{0;{otherwise}}\end{matrix}{qshft\_ upper}_{n}} = \left\{ {{\begin{matrix}{{{USB}_{n + 505} \cdot {fshft}_{{mod}{({n + {1,6}})}}};{{{for}\mspace{14mu} n} < 35}} \\{0;{otherwise}}\end{matrix}{pshft\_ lower}_{n}} = \left\{ {{\begin{matrix}{{{LSB}_{n - 7} \cdot {fshft}_{{mod}{({n + {5,6}})}}^{*}};{{{for}\mspace{14mu} n} > 7}} \\{0;{otherwise}}\end{matrix}{qshft\_ lower}_{n}} = \left\{ {{\begin{matrix}{{{LSB}_{n + 505} \cdot {fshft}_{{mod}{({n + {1,6}})}}^{*}};{{{for}\mspace{14mu} n} < 35}} \\{0;{otherwise}}\end{matrix}{for}\mspace{14mu} n} = {0,1\mspace{11mu}\ldots\;,42\mspace{14mu}{sample}\mspace{14mu}{index}\mspace{14mu}{for}\mspace{14mu}{each}\mspace{14mu}{successive}\mspace{14mu}{symbol}}} \right.} \right.} \right.} \right.$

STEP 2: These vectors are filtered with hqb, and then decimated by afactor of 4.

${p\_ upper}_{m} = {\sum\limits_{k = 0}^{22}\;{{pshft\_ upper}_{k + {4 \cdot m}} \cdot {hqb}_{k}}}$${q\_ upper}_{m} = {\sum\limits_{k = 0}^{22}\;{{qshft\_ upper}_{k + {4 \cdot m}} \cdot {hqb}_{k}}}$${p\_ lower}_{m} = {\sum\limits_{k = 0}^{22}\;{{pshft\_ lower}_{k + {4 \cdot m}} \cdot {hqb}_{k}}}$${q\_ lower}_{m} = {\sum\limits_{k = 0}^{22}\;{{qshft\_ lower}_{k + {4 \cdot m}} \cdot {hqb}_{k}}}$for  m = 0, 1, …  , 5

STEP 3: The “conjugate multiply and fold” operation is mathematicallydescribed for each upper or lower sideband by the following equations:

${u\_ upper}_{m} = {\sum\limits_{s = 0}^{S - 1}\;{{p\_ upper}_{m,s} \cdot {q\_ upper}_{m,s}^{*}}}$${u\_ lower}_{m} = {\sum\limits_{s = 0}^{S - 1}\;{{p\_ lower}_{m,s} \cdot {q\_ lower}_{m,s}^{*}}}$for  m = 0, 1, …  , 5where s is the folded symbol index, and S=16 symbols is the acquisitionblock size.

STEP 4: The normalization factor v is used to scale the DSQM to a 0 to 1range:

${v\_ upper}_{m} = {\sum\limits_{s = 0}^{S - 1}\;\left( {{{p\_ upper}_{m,s}}^{2} + {{q\_ upper}_{m,s}}^{2}} \right)}$${v\_ lower}_{m} = {\sum\limits_{s = 0}^{S - 1}\;\left( {{{p\_ lower}_{m,s}}^{2} + {{q\_ lower}_{m,s}}^{2}} \right)}$for  m = 0, 1,  …  , 5

STEP 5: The quality Q value for either the lower or upper sideband iscomputed as:

$Q_{U} = \frac{{{\sum\limits_{m = 0}^{5}\;{{u\_ upper}_{m} \cdot h_{m}}}}^{2}}{\left( {\sum\limits_{m = 0}^{5}\;{{v\_ upper}_{m} \cdot g_{m}}} \right)^{2}}$$Q_{L} = \frac{{{\sum\limits_{m = 0}^{5}\;{{u\_ lower}_{m} \cdot h_{m}}}}^{2}}{\left( {\sum\limits_{m = 0}^{5}\;{{v\_ lower}_{m} \cdot g_{m}}} \right)^{2}}$where filter coefficients h and the g are precomputed as:

${h = \begin{pmatrix}0.434 \\0.782 \\0.975 \\0.975 \\0.782 \\0.434\end{pmatrix}};$ and $g = {\begin{pmatrix}0.094 \\0.306 \\0.475 \\0.475 \\0.306 \\0.094\end{pmatrix}.}$

STEP 6: Finally, the composite DSQM metric is computed (0<DSQM<1).Notice that the additional sample timing condition is not imposed whenthe two sidebands are combined. This is because symbol synchronizationis assumed and the timing alignment is ensured by the symbol dispenser.DSQM=max[Q _(U) ,Q _(L),min{1,Q _(U) +Q _(L)−0.2}]

Next, the effect of DSQM quality threshold (Q) and peak sample delta(ΔP) threshold is examined. Simulation results were used to estimate theprobability of an individual (e.g., one sideband) DSQM symbol timingerror (135 samples/symbol) as a function of Cd/No. For the purpose ofthis analysis it is assumed that the timing error is relative to zero,and is defined over 135 samples ranging from −67 to +67. Negative timingerrors have the same probability as positive timing errors, so they arenot shown in the tables below. The timing error is assumed uniformoutside of ±5 samples, the cyclic prefix region.

Tables 4 through 7 show the conditional probabilityPsample(P,thres,Cd/No) that P is a particular one of the 135 possiblevalues, given that the quality threshold (i.e., 0.0, 0.1, 0.15, and 0.2)is exceeded (Q>thres) as characterized through simulation. The variableCd/No is the carrier to noise density ratio in units of dB_Hz. Althougha greater thres value discriminates against erroneous peaks, it alsoreduces successful acquisition probability for each DSQM trial. Noticethat Table 4 imposes no quality condition on DSQM quality thresholdsince thres=0.0 in this case.

TABLE 4 Probability of timing error when DSQM >0.0, Psample (P, 0.0,Cd/No) Timing Cd/No = Cd/No = Cd/No = Cd/No = Cd/No = Error P 50 dB- 51dB- 52 dB- 53 dB- 54 dB- (samples) Hz Hz Hz Hz Hz 0 0.175 0.285 0.4100.524 0.635 1 0.102 0.134 0.163 0.168 0.162 2 0.029 0.028 0.024 0.0140.006 3 0.010 0.0093 0.0051 0.0035 0.001 4 0.0059 0.0038 0.0028 0.000880.0005   5+ 0.0042 0.0029 0.0016 0.00081 0.00020

TABLE 5 Probability of timing error when DSQM >0.1, Psample (P, 0.1,Cd/No) Timing Cd/No = Cd/No = Cd/No = Cd/No = Cd/No = Error P 50 dB- 51dB- 52 dB- 53 dB- 54 dB- (samples) Hz Hz Hz Hz Hz 0 0.256 0.383 0.4800.562 0.649 1 0.151 0.171 0.183 0.178 0.163 2 0.038 0.033 0.023 0.0140.0053 3 0.012 0.0092 0.0048 0.0028 0.0011 4 0.0046 0.0030 0.00160.00088 0.00026   5+ 0.0026 0.0015 0.00075 0.00038 0.0000900

TABLE 6 Probability of timing error when DSQM >0.15, Psample (P, 0.15,Cd/No) Timing Cd/No = Cd/No = Cd/No = Cd/No = Cd/No = Error P 50 dB- 51dB- 52 dB- 53 dB- 54 dB- (samples) Hz Hz Hz Hz Hz 0 0.427 0.503 0.5380.605 0.672 1 0.189 0.205 0.201 0.184 0.158 2 0.028 0.022 0.019 0.00940.0039 3 0.012 0.0043 0.00040 0.0012 0.00033 4 0.0014 0.0014 0 0 0   5+0.00088 0.00025 0.00017 0.000052 0.000018

TABLE 7 Probability of timing error when DSQM >0.2, Psample (P, 0.2,Cd/No) Timing Cd/No = Cd/No = Cd/No = Cd/No = Cd/No = Error P 50 dB- 51dB- 52 dB- 53 dB- 54 dB- (samples) Hz Hz Hz Hz Hz 0 0.477 0.565 0.5500.609 0.701 1 0.215 0.199 0.203 0.188 0.147 2 0.031 0.016 0.021 0.00540.0027 3 0.0077 0 0 0.0011 0 4 0 0 0 0 0   5+ 0.00012 0.000049 0.0000190.0000085 0

The probability of a particular timing error when no signal is presentis independent of thres, and is simply the uniform probability ofselecting any one of the 135 sample timing offsets.

${{Psample}\;\left( {P,0,0} \right)} = {{{Psample\_ no}{\_ sig}} = {\frac{1}{135} \cong 0.0074}}$

The probability that one DSQM quality measurement exceeds the threshold(Q>thres) for a given Cd/No is defined as P1(thres,Cd/No). Thisparameter is a function of thres and Cd/No as characterized throughsimulation; results are shown in Table 8.

TABLE 8 Probability of exceeding DSQM threshold, P1(thres, Cd/No) Cd/Cd/ Cd/ Cd/ Cd/ DSQM No No = 50 No = 51 No = 52 No = 53 No = 54 thressignal dB-Hz dB-Hz dB-Hz dB-Hz dB-Hz 0.10 0.261  0.434 0.542 0.724 0.8510.947 0.15 0.022  0.093 0.175 0.316 0.530 0.760 0.20 0.0015 0.016 0.0400.103 0.232 0.470

Acquisition Using Multiple DSQM Measurements

The acquisition probability is the joint probability that a pair of peakindices (e.g., P_(U) or P_(L)) is within D samples of each other, giventhat at least one quality measurement exceeds thres. This can beanalyzed from the sample timing offset Psample data. For given values ofthres and Cd/No, this probability is computed using the probabilities inTables 3 through 7.

${{Pacq}\left( {D,{thres},{{Cd}\text{/}{No}}} \right)} = {{{2 \cdot P}\; 1{\left( {{thres},{{Cd}\text{/}{No}}} \right) \cdot \left( {1 - {P\; 1\left( {{thres},{{Cd}\text{/}{No}}} \right)}} \right) \cdot {\sum\limits_{P = {- 67}}^{67}\;\begin{bmatrix}{{{Psample}\left( {P,{thres},0} \right)} \cdot \sum\limits_{d = {- D}}^{D}} \\{\;{{Psample}\left( {{P + d},{thres},{{Cd}\text{/}{No}}} \right)}}\end{bmatrix}}}} + {P\; 1{\left( {{thres},{{Cd}\text{/}{No}}} \right)^{2} \cdot {\sum\limits_{P = {- 67}}^{67}\;\begin{bmatrix}{{{{Psample}\left( {P,{thres},{{Cd}\text{/}{No}}} \right)} \cdot \sum\limits_{d = {- D}}^{D}}\;} \\{{Psample}\left( {{P + d},{thres},{{Cd}\text{/}{No}}} \right)}\end{bmatrix}}}}}$

The expression above indexes the sample timing data for Psample slightlyabove 67 samples and below −67 samples. In these cases there is a modulowrap-around where sample 68 is equivalent to −67, and sample −68 isequivalent to 67. However, since the probability is uniform outside of±4 samples, these values of Psample are held constant. So any index forPsample outside of ±4 has an index equivalent to P=5. Notice that Pacqdoes not guarantee that all acquisitions have an acceptable sampletiming error, although the pair of timing P measurements is within Dsamples of each other. So the probability Pacq includes a small fractionof acquisitions where the sample timing error is faulty, leading to a“Badtrack” condition.

If the initial symbol timing error is greater than 3 samples, then thesymbol tracking will likely converge to a faulty stable sample offset(about 27 samples error), resulting in a “Badtrack.” The Badtrackcondition sometimes occurs at low SNR when the error is 3 samples, andthe symbol clock frequency error could also affect the probability ofBadtrack. Therefore a more conservative condition requiring less than 3samples timing error for proper tracking is analyzed. The probability ofBadtrack is conditioned on passing the requirements for detectingacquisition, but the timing estimate error is outside of ±2 samples. Theprobability of Badtrack is expressed as

${{Pbadtrack}\left( {D,{thres},{{Cd}\text{/}{No}}} \right)} = {{{4 \cdot P}\; 1{\left( {{thres},{{Cd}\text{/}{No}}} \right) \cdot \left( {1 - {P\; 1\left( {{thres},{{Cd}\text{/}{No}}} \right)}} \right) \cdot {\sum\limits_{P = 3}^{67}\;\begin{bmatrix}{{{{Psample}\left( {P,{thres},0} \right)} \cdot \sum\limits_{d = {- D}}^{D}}\;} \\{{Psample}\left( {{P + d},{thres},{{Cd}\text{/}{No}}} \right)}\end{bmatrix}}}} + {{2 \cdot P}\; 1{\left( {{thres},{{Cd}\text{/}{No}}} \right)^{2} \cdot {\sum\limits_{P = 3}^{67}\;\begin{bmatrix}{{{Psample}\;{\left( {P,{thres},{{Cd}\text{/}{No}}} \right) \cdot \sum\limits_{d = {- D}}^{D}}}\;} \\{{Psample}\left( {{P + d},{thres},{{Cd}\text{/}{No}}} \right)}\end{bmatrix}}}}}$

Then the probability of a good acquisition where the timing falls within−2≦P≦2 is:Pgoodacq(D,thres,Cd/No)=Pacq(D,thres,Cd/No)−Pbadtrack(D,thres,Cd/No).

Since Pbadtrack is generally much smaller than Pacq for the casesexamined here, Pgoodacq is only slightly smaller than Pacq.

FIG. 16 shows the probability of a good acquisition where the DSQMtiming error is P≦2 samples. FIG. 17 shows the probability of a badacquisition where the DSQM timing error is P>2 samples.

The probability of false alarm occurs when no signal is present, atleast one of the pair of DSQM quality measurements exceeds thethreshold, and ΔP≦D. This is equivalent to the expression for Pacq whenno signal is present.

which can also be expressed as:

${{Pfalsealarm}\left( {D,{thres}} \right)} = {\left( {1 - \left\lbrack {1 - {P\; 1\left( {{thres},0} \right)^{2}}} \right\rbrack} \right) \cdot \frac{{2 \cdot D} + 1}{135}}$

TABLE 9 Probability of false alarm (ΔP ≦ D) with no signal, Pfalsealarm(D, thres) thres D = 1 D = 2 0.00 0.022 0.037 0.10 0.010 0.017 0.150.001 0.0016 0.20 0.000067 0.00011

Temporal Consistency

The temporal consistency check is intended for acquisition of a signalwhere one sideband is severely corrupted. The corrupted sideband isassumed to yield an unreliable symbol timing offset value P, so the ΔP≦Dcondition is unlikely to be satisfied. The DSQM decision rule requires atiming consistency within ΔP≦D samples for a pair of DSQM measurements.This pair of DSQM measurements normally consists of the upper and lowersideband values. However, if this consistency is not met for the pair ofsidebands, then the next pair of DSQM samples is also used to check fortemporal consistency on the same sideband. Furthermore, this temporalconsistency requires only the most recent DSQM value to exceed thethreshold, while the previous value on the same sideband must be within±D samples. There is no requirement that the previous value exceeds thethreshold. This temporal consistency condition will tend to increase allthe acquisition probabilities (Pacq, Pbadtrack, Pgoodtrack andPfalsealarm), especially for low values of Cd/No. For low Cd/No in AWGN,these probabilities are expected to nearly double due to the temporalconsistency check. The doubling can be explained by allowing an extracheck for ΔP≦D on the same sideband in addition to the alternatesideband. For low Cd/No, only one sideband is likely to exceed thethreshold. Then the probability of a false alarm, including the temporalconsistency check, is modified to approximately

${{Pfalsealarm}\left( {D,{thres}} \right)} = {2 \cdot \left( {1 - \left\lbrack {1 - {P\; 1\left( {{thres},0} \right)^{2}}} \right\rbrack} \right) \cdot \frac{{2 \cdot D} + 1}{135}}$Table 10 is similar to Table 9, except the probability of false alarmincludes the temporal consistency check.

TABLE 10 Probability of false alarm (ΔP ≦ D) with temporal consistency,no signal, Pfalsealarm (D, thres) thres D = 1 D = 2 0.00 0.044 0.0740.10 0.020 0.034 0.15 0.002 0.0032 0.20 0.000134 0.00022

Frame Synchronization Analysis

Frame synchronization is described here as a two-step process: InitialSubframe Found, followed by Subframe Lock. This process starts after asuccessful DSQM detection identifies the symbol timing offset, and thesymbol-synchronized OFDM demodulation commences. However, if an InitialSubframe is not detected after a predetermined time following DSQMacquisition, then a reacquisition must be initiated to prevent sampletiming drift caused by clock frequency error.

To detect the Initial Subframe, the receiver performs a slidingcorrelation over all the OFDM subcarriers and the received OFDM symbols.The correlation is for an 11-bit sync pattern spread over a 32-symbolSubframe in all of the Reference Subcarriers. A subcarrier correlationis declared when all 11 sync bits match the sync pattern for thatsubcarrier. Initial Subframe Found is declared when correlation issuccessful on a predetermined number of subcarriers spaced a multiple of19 subcarriers apart, and on the same 32-bit subframe. When InitialSubframe Found occurs, the 32-bit subframe boundaries are established,as well as the location of the Reference Subcarriers. If the Subframe isnot found after a predetermined time after DSQM acquisition, then thisprocess is terminated, and a reacquisition is initiated.

Subframe Lock is established when another predetermined number ofsubcarrier correlations occurs on the established Reference Subcarriers,and are spaced from the Initial Subframe Found by an integer multiple of32 symbols. If the symbol tracking is initiated immediately afterInitial Subframe Found, then it may not be necessary to place a timelimit on Subframe Lock before a reacquisition. This is because furthersymbol timing drift is prevented by symbol tracking.

The following analysis characterizes the probabilities associated withInitial Subframe Found and Subframe Lock. This can be combined with theDSQM analysis to determine the probabilities of successful acquisition,faulty acquisition, and estimates of the time required for SubframeLock.

First compute correlation probability on one subcarrier with 11 syncbits. Because of the possibility of large phase errors due to initialsymbol error (before symbol tracking converges), one must consider the 4possible phases of the signal (I, Q and complements) for correlationpossibilities. Note that this 4-phase detection method may introduceother error conditions when 2 phases straddle the boundary. Thisprobability is approximated by:Psync(BER)=1−[1−(1−BER)¹¹]·(1−BER¹¹)·(1−0.5¹¹),where the probability of bit error (BER) for differentially detectedBPSK, or DBPSK is

${BER} = {{- \frac{1}{2}} \cdot {{\mathbb{e}}^{{- {Eb}}\text{/}{No}}.}}$

For the BPSK reference subcarrier of the IBOC signal, the relationshipbetween Eb and Cd in dB is:Eb _(dB) =Cd _(dB)−51 dB.

The quantity Cd/No is expressed in units of dB_Hz. Then the BER can beexpressed as a function of Cd/No.

${BER} = {{- \frac{1}{2}} \cdot {\mathbb{e}}^{- 10^{\lbrack{{({{{Cd}\text{/}{No}} - 51})}\text{/}10}\rbrack}}}$

In order to compute the probability of Initial Subframe Found andSubframe Lock, some intermediate probabilities are computed. Theprobability that a successful correlation occurs on Nsc subcarriers,given that the Primary reference subcarriers are already identified, andare synchronized to the Subframe boundary is:

${{Psf}\left( {{Nsc},{BER}} \right)} = {\sum\limits_{n = {Nsc}}^{22}\;{\left( {{\frac{22!}{{n!} \cdot {\left( {22 - n} \right)!}} \cdot {Psync}}\;{({BER})^{n} \cdot \left\lbrack {1 - {{Psync}\;({BER})^{22 - n}}} \right\rbrack}} \right).}}$

The probability Psf is also the conditional probability of Subframe Lockin any one Subframe time (32 symbol period), given that Initial SubframeFound is successful.

Allowing for all 19 possible Reference Subcarrier offsets in apartition, and for all 32 symbol possibilities in a Subframe, theaverage probability of Initial Subframe Found over every 32-symbol shiftof a subframe is:Pfound(Nsc,BER)=1−[1−Psf(Nsc,BER)]·[1−Psf(Nsc,0.5)]^(19·32-1)

The average time (seconds) required for Initial Subframe found, giventhat the signal is acquired and no reacquisitions are allowed, can becomputed as:

${{Tfound}\left( {{Nsc},{BER}} \right)} = {\frac{32}{{{fsym} \cdot {Pfound}}\;\left( {{Nsc},{BER}} \right)}.}$where fsym is the OFDM symbol rate. The plot of FIG. 19 showsTfound(Nsc,BER) for Reference Subcarrier correlation thresholds of 4, 3,and 2 over a range of Cd/No.

FIG. 18 is a plot showing the average time required for Subframe lockafter Initial Subframe found. This assumes no reacquisitions.

The average time (seconds) required for Subframe Lock, given InitialSubframe Found, can be computed as:

${{Tsf}\left( {{Nsc},{BER}} \right)} = {\frac{32}{{{fsym} \cdot {Psf}}\;\left( {{Nsc},{BER}} \right)}.}$

The plot of FIG. 19 shows Tsf(Nsc,BER) for Reference Subcarriercorrelation thresholds of 4, 3, and 2 over a range of Cd/No.

The probability of Initial Subframe found over the allotted Nsf1Subframe periods to find the sync pattern is:PfoundNsf(Nsc1,BER,Nsf1)=1−(1−Pfound(Nsc1,BER))^(Nsf1).

The probability of Subframe Lock over the allotted Nsf2 Subframe periodsis:PlockNsf(Nsc2,BER,Nsf2)=1−(1−Psf(Nsc2,BER))^(Naf2).

Selection of Parameter Values for Frame Sync

Based on the probability analyses in the previous sections, thefollowing parameter values are recommended:

D=1 Sample offset difference (ΔP≦D) permitted

thres=0.1 DSQM quality threshold for acquisition

Nsc1=3 Number of sync correlations required for Initial Subframe Found

Nsc2=2 Number of sync correlations required for Subframe Lock

Nsf1=4 Number of Subframes for Initial Subframe Found before reacq

Nsf2=4 Number of Subframes for Subframe Lock before reacq

False Acquisition and Subframe Lock Rate

It was shown in the DSQM analysis that the probability of false DSQMacquisition (with no signal) Pfalsealarm is approximately 0.02(thres=0.1, D=1, including temporal consistency check) for every16-symbol period. Then the average time between false DSQM acquisitionsis:

${TfaDSQM} = {\frac{16}{{{fsym} \cdot {Pfalsealarm}}\;\left( {1,0.1} \right)} = {2.3\mspace{14mu}{{seconds}.}}}$

The probability of Initial Subframe Found (no signal) within the 4Subframes allotted is:PfoundNsf(3,0.5,4)=0.027.

The time period allotted (Nsf Subframes) for Initial Subframe Found is:

${{{TNsf}({Nsf})} = \frac{32 \cdot {Nsf}}{fsym}};$ andTNsf(4) = 0.372  seconds.

The average time required for faulty Initial Subframe Found, given afaulty DSQM acquisition (BER=0.5) is:

${{TfoundNsf}\left( {{{Nsc}\; 1},{{Nsf}\; 1}} \right)} = \frac{{{TNsf}\;\left( {{Nsf}\; 1} \right)} + {TfaDSQM}}{{PfoundNsf}\;\left( {{Nsc}\; 1,0.5,{Nsf}\; 1} \right)}$TfoundNsf (3, 0.5, 4) = 100  seconds.

The probability of faulty Subframe Lock over the allotted Nsf=4Subframes, given a faulty Initial Subframe found, is:PlockNsf(2,0.5,4)=3.4·10⁻³.

The time period allotted (Nsf Subframes) for Subframe Lock in this caseis the same as for Initial Subframe Found:TNsf(4)=0.372 seconds.

The average time required for faulty Subframe Lock, given a faulty DSQMacquisition (BER=0.5) and faulty Initial Subframe Found is:

${{TlockNsf}\left( {{{Nsf}\; 2},{{Nsf}\; 2}} \right)} = \frac{{{TfoundNsf}\left( {{Nsc}\; 2,0.5,{Nsf}\; 2} \right)} + {TfaDSQM}}{{PlockNsf}\;\left( {{Nsc}\; 2,0.5,{Nsf}\; 2} \right)}$TlockNsf(3, 0.5, 4) = 29, 329  seconds, or  about  8  hours.

Then false Subframe Lock occurs about once in 8 hours with no signalpresent. However, it is also assumed that symbol tracking doesn't resultin a false lock, which is influenced by the sample clock error (e.g., upto 100 ppm). A combination of large clock error and initial sampleoffset error from DSQM could result in a false lock in symbol tracking,or “Badtrack”. A means of detecting Badtrack should be implemented.

VII. DSQM-Lite for Badtrack Detection

A Badtrack detection method is needed to prevent the demodulator fromremaining in a stuck condition while outputting faulty branch metrics.Badtrack is the result of the symbol tracking being stuck at a faultysample offset (e.g. 27 samples error). This is due to a 2-π phase shift(instead of 0) between adjacent Reference Subcarriers. The Badtrack isespecially important in an MRC diversity receiver where each demodulatorcan operate at a lower SNR, and contamination of one demodulator in aBadtrack state to the other demodulator is possible. A reacquisition isinvoked when a Badtrack is detected. The existing fourth-power Badtrackdetection method is unreliable for Cd/No<54 dB_Hz. However aDSQM_lite-based detection method is more reliable, and is describedhere. The DSQM_lite function provides periodic digital signal qualitymetrics (every 16 or 32 symbols), but requires fewer MIPS than theoriginal DSQM function. Fewer MIPS are needed because it exploitsknowledge of the location of the cyclic prefix region after initialacquisition.

Assume DSQM_lite samples are available every 16-symbol period. These canbe filtered with a unity-gain lossy integrator with a time constant ofabout 8 samples. At the start of DSQM_lite filtering, the filter memoryDSQM_lite_filt should be initialized to DSQM_lite_filt_init (e.g.,0.08), which is between the two threshold values for Badtrack detectionand low signal suppression described later in this section. The filterinitialization (instead of zero) reduces the initial period when a goodsignal is suppressed due to filter time constant. The DSQM_lite IIRfilter is a unity-gain lossy integrator with a time constant of about 8DSQM_lite samples (128 symbols). The filter expression is:DSQM_lite_filt_(n)=0.875·DSQM_lite_filt_(n-1)+0.125·DSQM_lite_(n).

Branch metrics can be suppressed (zeroed) whenDSQM_lite_filt<thres_nosig. (e.g., thres_nosig=0.1) The DSQM_lite_filtvalue approaches approximately 0.15 for Cd/No=51 dB_Hz, the minimumexpected operating value.if DSQM_lite_filt_(n)<thres_nosig; then ZERO all Branch metrics.

A counter is incremented when the filtered DSQM_lite_filt<thres_badtrack(e.g., thres_badtrack=0.06). This threshold value offers sufficientmargin for Badtrack detection since DSQM_lite_filt approachesapproximately 0.03 in a Badtrack condition or when no signal is present.This should be effective in preventing contamination to the alternatedemodulator in the MRC case.

Reacquisition is invoked when the counter indicates a sufficiently longduration. The counter is initialized to zero at DSQM acquisition, andreset to zero whenever the filtered DSQM_lite_filt≧thres_badtrack.

${Badtrack\_ count}_{n} = \left\{ \begin{matrix}{{{Badtrack\_ count}_{n - 1} + 1};{{{if}\mspace{14mu}{DSQM\_ lit}{\_ filt}_{n}} < {thres\_ badtrack}}} \\{0;{otherwise}}\end{matrix} \right.$if Badtrack_count_(n)>100, then invoke reacquisition (about 4.6 sec)

FIG. 20 shows a plot of DSQM_lite_filt versus time (in DSQM periods) forCd/No=51 dB_Hz. The horizontal axis units are in DSQM samples, whereeach sample spans 16 symbols (46.5 msec). The average value approachesabout 0.15 in this case. FIG. 21 shows a plot of DSQM_lite_filt versustime (in DSQM periods) for no signal present (noise only). The averagevalue approaches about 0.03 when no signal is present. The horizontalaxis units are in DSQM samples, where each sample spans 16 symbols (46.5msec).

FIGS. 22 through 24 show DSQM_lite_filt at 51 dB_Hz with differentvalues of symbol timing error. The symbol tracking was disabled in thesecases, and the symbol timing error was held constant. The degradationdue to symbol timing error can be assessed by comparing theDSQM_lite_filt value to FIG. 20. FIG. 20 shows that the DSQM_lite_filtapproaches approximately 0.15 when no sample error is present. FIGS. 22through 24 show that the DSQM_lite_filt approaches approximately 0.12,0.08 and 0.05 with sample offset errors of 4, 8, and 12 samples,respectively, at 540 samples/symbol. The BER (after FEC decoding)measured at 8 samples offset is approximately 0.5 for a single (non-MRC)modem, indicating that the branch metrics may provide insignificantimprovement for MRC combining. That is why the DSQM_lite_filt thresholdfor branch metric suppression is set at the particular value ofthres_nosig.

VIII. Implementation Considerations

Since the pair of digital demodulators may not be in the same state(e.g. reacq, frame sync, valid branch metrics) at the same time, anarbitration scheme must be developed. One possibility is that bothdigital demodulators (D0 and D1) operate mostly autonomously from eachother. The first demod to reach Subframe Lock shall coordinateoperations (master) for combining branch metrics, and downstream(deinterleaving, decoding, etc.). Branch metrics can be combined fromalternate demods when available. It is assumed that the demodulationprocess is multiplexed by alternating symbol processing for the pair ofdemodulators. Then only one demodulator at a time will change the state.Transitions between states can be initiated either by a reacquisition(reacq) or a Subframe Lock (SFLock). Each demodulator can be in only oneof two modes, SYNC or DECODE. For each demodulator the SYNC mode isentered by a reacq, and the DECODE mode is entered by a SFLock.

FIG. 25 is a state diagram for MRC coordination and arbitration. Thereare 4 possible states for the MRC Arbitration State diagram shown inFIG. 25. The state is determined by the pair of demodulator modes.

The downstream functions (deinterleaving, decoding, etc.) areinitialized in State 0. Upon entering State 0, the deinterleaver is notreceiving symbols from either of the demodulators, since they are bothin SYNC mode. The first demodulator to establish Subframe Lock initiatesthe downstream functions. The last demodulator to enter SYNC modedisables the downstream functions.

The described acquisition and tracking modifications will allow morereliable acquisition and tracking at lower SNRs to aid MRC performance.Reducing DSQM threshold from 0.2 to 0.1 will improve acquisition time atlow SNR.

All fourth-power-based processing has been eliminated, including symboltracking and bad-track detection/reacquisition control.

The symbol tracking algorithm is disabled until Initial Subframe Found.The symbol sample offset correction determined by DSQM is maintained.The sample timing may drift due to the difference in transmitter andreceiver clocks (e.g., 100 ppm will drift 18.6 samples/second at 186ksps). The symbol tracking is intended to prevent further sample errordrift after Initial Subframe Found. One sample at a time is corrected.The receiver allows the sample slip to drift for a limited time until itis out of symbol tracking range. If it drifts any longer then areacquisition is performed.

Before Initial Subframe Found, the symbol tracking loop input and symboltracking SNR should be 0. After Initial Subframe Found, symbol trackingon reference subcarriers can begin.

Filtered sync weights can be used immediately upon starting the symboltracking loop. All canned weights (4^(th) power and pilot) can bedeleted. Initializing sync weights to canned weights instead of zero canbe considered.

The fast-track period, with the symbol tracking loop gain collapsingfrom 0.2 to 0.02, can also start immediately after Initial SubframeFound. It can remain 400 symbols long. However, other actions previouslyperformed during fast-track are deleted. Since tracking on pilots, thesymbol tracking error input is scaled by 1/19. The symbol tracking errorinput is clipped to ±1 (it was previously clipped to ±5 duringfast-track). The SNR-based flywheel gain shall be set to 1 during thefast-track period (until proportional gain=0.02).

Disable all SNR-based reacquisition conditions. Note that SNR=0 until 21symbols after Init Subframe Found. In Initial Subframe Detection state,remove reacq if SNR<0.1 and no subframes detected within 100 symbols. InSubframe Verification state, remove reacq if 125 symbols have beenprocessed since entering this state, and SNR<0.1.

The rules for determining Subframe Found and Lock have been modified.The Initial Subframe Found requires only three 11-bit sync correlationsspaced by 19 subcarriers. If not detected within 128 symbols (4 Subframeperiods) after successful DSQM, then perform a reacquisition. TheSubframe Lock checks only the identified reference subcarriers frominitial subframe correlation at multiples of the 32-symbol spacing.

Only the current subframe spacing needs to be checked against theinitially detected subframe, not all previously detected subframes. The32-subframe array can be removed.

The second subframe requires only two 11-bit sync correlations. IfSubframe lock is not established within 128 symbols (4 Subframes) afterInitial Subframe Found, then perform a reacquisition.

The Reference Subcarrier ID (coarse bin offset) can be checked forconsistency between the Initial Subframe Found and 2^(nd) detectedsubframe, before declaring Subframe Lock. A reacquisition can beperformed if the Reference Subcarrier IDs are different.

Bad-track detection can be implemented using IIR-filteredDSQM_lite_filt, replacing fourth-power bad-track detection. Areacquisition can be invoked when bad-track is detected.

DSQM can be calculated every 16 symbols. IIR can be a single poleunity-gain lossy integrator with alpha=⅛. Filter can be initialized toDSQM_lite_filt_init (e.g., 0.03 to 0.08).

A counter can be incremented when the filteredDSQM_lite_filt<thres_badtrack (e.g., 0.06). A reacquisition can beinvoked when the counter exceeds 100 DSQM periods (1600 symbols). Thecounter can be reset to 0 when filtered DSQM-lite exceedsthres_badtrack. The timeout after Subframe lock may be increased.

Whenever the filtered DSQM_lite_filt<thres_nosig (e.g.,0.6≦thres_nosig≦0.1), all branch metrics can be zeroed. The onlyoriginal Synchronization Control Reacq condition that remains is the648-subframe (one minute) timeout in the Subframe Lock state.

The other mode fields (similar to Reference Subcarrier ID) between theInitial Subframe Found and Subframe Lock can be checked for consistencyand a reacquisition can be performed if they are inconsistent.

While the invention has been described in terms of various embodiments,it will be apparent to those skilled in the art that numerous changescan be made to the disclosed embodiments without departing from thescope of the claims set forth below. For example, those skilled in theart will understand that the functions and processes described hereincan be implemented using known circuit components and/or one or moreprocessors programmed to perform the functions or processes.

What is claimed is:
 1. A method for processing a radio signalcomprising: receiving a signal on two antennas; demodulating the signalusing first and second independent signal paths that are synchronized bysymbol number; maximum ratio combining branch metrics from the tworeceiver paths; and using the combined branch metrics to produce anoutput, wherein a first one of the first and second independent signalpaths to reach Subframe Lock coordinates operations for maximum ratiocombining the branch metrics and downstream operations.
 2. The method ofclaim 1, wherein the first and second signal paths adjust the magnitudesof the first and second branch metrics in response to a signal-to-noiseratio of the signal in the first and second signal paths.
 3. The methodof claim 1, wherein the maximum ratio combining step sums corresponding,synchronized branch metrics from the first and second independent signalpaths.
 4. The method of claim 1, wherein when one of the signal pathshas no branch metrics available, the branch metrics of that signal pathare zeroed.
 5. A method for processing a radio signal comprising:receiving a signal on two antennas; demodulating the signal using firstand second independent signal paths that are synchronized by symbolnumber; maximum ratio combining branch metrics from the two receiverpaths; and using the combined branch metrics to produce an output,wherein the first and second independent signal paths each include ademodulator and only one of the demodulators at a time changes itsstate.
 6. The method of claim 5, wherein transitions between states isinitiated either by a reacquisition or a Subframe Lock.
 7. The method ofclaim 5, wherein each of the demodulators can be in only one of twomodes, SYNC or DECODE.
 8. The method of claim 7, wherein the SYNC modeis entered by a reacquisition, and the DECODE mode is entered by aSubframe Lock.
 9. A receiver comprising: first and second inputsconfigured to receive a signal on two antennas; and first and seconddemodulators for demodulating the signal in first and second independentsignal paths that are synchronized by symbol number; and circuitry formaximum ratio combining branch metrics from the two signal paths, andusing the combined metrics to produce an output, wherein a first one ofthe first and second independent signal paths to reach Subframe Lockcoordinates operations for maximum ratio combining the branch metrics,and downstream operations.
 10. The receiver of claim 9, wherein thefirst and second signal paths adjust the magnitudes of the first andsecond branch metrics in response to a signal-to-noise ratio of thesignal in the first and second signal paths.
 11. The receiver of claim9, wherein the maximum ratio combining sums corresponding, synchronizedbranch metrics from the first and second independent signal paths. 12.The receiver of claim 9, wherein when one of the signal paths has nobranch metrics available, the branch metrics of that signal path arezeroed.
 13. A receiver comprising: first and second inputs configured toreceive a signal on two antennas; and first and second demodulators fordemodulating the signal in first and second independent signal pathsthat are synchronized by symbol number; and circuitry for maximum ratiocombining branch metrics from the two signal paths, and using thecombined metrics to produce an output, wherein only one of thedemodulators at a time changes its state.
 14. The receiver of claim 13,wherein transitions between states is initiated either by areacquisition or a Subframe Lock.
 15. The receiver of claim 13, whereineach of the demodulators can be in only one of two modes, SYNC orDECODE.
 16. The receiver of claim 15, wherein the SYNC mode is enteredby a reacquisition, and the DECODE mode is entered by a Subframe Lock.